Statement A,B is true rest all statement are false about the given function.
Given the function: [tex]2x^3+8[/tex]
Statement A:
The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value).
For the function 2x^3 + 8, the domain is all real numbers, which is represented as (-infinity, +infinity).
It is because the expression inside the function, 2x^3, is defined for all real numbers.
so above statement is true.
Statement B:
statement A and B are same so it's also true.
Statement C:
The range of a function is the set of all possible output values (y-values) that the function can produce.
For the function 2x^3 + 8, the range is also all real numbers (-infinity, +infinity)
It is because the function is a polynomial of odd degree (3) and it does not have any restriction on the output value. Since the function does not have any restriction, it can take any real number as an output value and thus the range is all real numbers.
so this statement is false.
Statement D:
The y-intercept of the function 2x^3 + 8 is 8. It is the point at which the graph of the function crosses the y-axis, which occurs when x = 0. So when x = 0, y = 2(0)^3 + 8 = 8.
so this statement if false.
Statement E:
A function has a center of symmetry if it is unchanged (i.e. is symmetric) when reflected across a line or point. The line or point across which the function is symmetric is called the axis of symmetry or center of symmetry.
The function 2x^3 + 8 does not have a center of symmetry. It is because the function is a polynomial of odd degree and it does not have any symmetry. The polynomials of odd degree are not symmetric about any point or line.
So this statement is also false.
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Determine and state an equation of the line perpendicular to the line 5x-4y=10 and passing through the point (5,12)
The equation of the line perpendicular to the line 5x-4y=10 and passing through the point (5,12) is y = 4x/5 + 8.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given:
The line 5x-4y=10.
Simplifying,
y = (-5/4)x + 5/2
Comparing with the slope-intercept form,
y = mx + b,
where m is the slope and b is y-intercept.
The slope is = -5/4
The slope of the perpendicular line,
= negative reciprocal of the slope of the line where the line is perpendicular.
= 4/5
So, the line:
If a line passes through one point (x₁ ,y₁) and have slope m,
then the equation of line is
y - y₁ = m (x - x₁)
y - 12 = (4/5)(x-5)
y = 4x/5 + 8
Therefore, the equation of the line is y = 4x/5 + 8
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what part of 3$ is the sum of 7 dimes, 1 nickel and 3 pennies?
Answer:
7/60
Step-by-step explanation:
First, we would need to add up all of the coins and know their values.
1 dime (d) = 10¢
1 nickel (n) = 5¢
1 penny (p) = 1¢
An equation we can use will look something like this:
(d × 7) + (n × 1) + (p × 3) =?
Now just add the numbers and solve.
(10 × 7) + (5 × 1) + (1 × 3) = 78
Therefore, the total amount is 78¢.
Now to figure out how much 78¢ is out of $3, we can use an equation that looks something like this:
3 ÷ 0.78 = 3.84615385 or 7/60
So, this means that with 7 dimes, 1 nickel and 3 pennies it is 7/60 of $3.
Consider the division of 8y2 - 12y + 4 by 4y.
What are the values of a and b?
=a+b++
O a = 2y and b = 3
O a= { and b = -3y
O a= 2y and b = -3
O a = ? and b = 3y
Mark this and return
Save and Exit
Next
Sub
By solving the given Algebraic expression, the correct answer is Option (C) ,a = 2y and b = –.
What is an Algebraic Expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are different components of an algebraic expression. Let us have a look at the image given below in order to understand the concept of Variables, Constants, Terms, and Coefficients of any algebraic expression.
Assume that 8y2 - 12y + 4 has terms with a=8y² , b=-12y, c=4
Now, to divide 8y2 - 12y + 4 by the monomial (single term) 4y,
The easy way is divide each term of the dividend by the monomial:
8y2 - 12y + 4 /4y
=(8y²-12y+4)/4y
=(8y²/4y)-(12y/4y)+(4/4y)
=2y-3+1/y
After performing the division we get that now a = 2y and b = –3
We can conclude that the correct answer is a = 2y and b = –3
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It takes 34 of an hour to paint a single shutter. It takes 9 hours to paint 12 pairs of shutters. The number of hours, y, that it takes to paint xshutters shows either a direct or inverse variation. What is the equation that relates x and y?
The equation that relates x and y for the given data is y = (3/4)x.
The relationship between the number of shutters (x) and the number of hours (y) is an inverse variation because as the number of shutters increases, the number of hours required to paint them decreases and vice versa.
An inverse variation is a relationship between two variables in which their product is always equal to a constant value. Mathematically, it can be represented by the equation: y = k/x where k is a constant and x and y are the variables in question.
Hence, the equation that relates x and y can be found using the information given:
y = (9 hours) / (12 shutters) * x shutters
y = (3/4)x is the required equation.
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which set of ordered pairs below is a function?
The first and the third set of order pairs is a function.
What is function?
A set of ordered pairs that contain only unique ordered pairs with unique x coordinates is referred to as a function. A function is defined by an equation that generates a set of ordered pairs.
Consider, the given set of order pairs,
I - {(3, 3), (6, 1), (2, 3)}
II - {(4, 7), (2, 8), (4, 2)}
III - {(9, 6), (3, 1), (7, 3)}
We have check which set of ordered pairs above is a function.
Since, a function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate.
In the given order pairs the second order pair contain same x - coordinate.
So, the second order pair is not a function.
Hence, the first and the third set of order pairs is a function.
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In 2003 how many African American students attended a school with over 90% of its population being a minority?
According to ProPublica, from 1993 to 2011, there were almost 2.9 million black pupils enrolled in schools where at least 90% of the student body is made up of minorities.
Explain about the minority?The absence of a majority on the territory of a State is indicated by a minority. That essentially indicates that less than 50% of a nation's population belongs to one or more ethnic, religious, or linguistic groups.
According to Section 2(c) of the National Commission for Minorities Act of 1992, the following groups have been designated as minority communities: Muslims, Sikhs, Christians, Buddhists, Jain, and Zorastrians. According to the Census of 2011, minorities make up around 19.3% of the overall population of the nation.
The term "minority" in the 1990s typically refers to four significant racial and ethnic groups: African Americans, American Indians and Alaska Natives, Asians and Pacific Islanders, and Hispanics.
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I need some help with the problem from my math class (-4w - 7)5
-20w-35
I used the distributive property to distribute terms, and then simplified
Margo borrows $700, agreeing to pay it back with 8% annual interest after 16 months. How
much interest will she pay?
After 16 months, Margo will pay $74.67 interest
We know that the simple Interest Formula
I = P × r × t
Where: P = Principal Amount
I = Interest Amount
R = Rate of Interest as a percent
r = Rate of Interest in decimal
r = R/100
t = Time Periods involved
Here we have been given P = $700, t = 16 months and R = 8%
First we convert interest rate R percent to r a decimal
r = R/100
= 0.08 per year,
Now we convert time from months to years .
16 months ÷ 12 months/year
= 1.333333 years,
Using above formula of simple interest,
I = P × r × t
I = 700 × 0.08 × 1.333333
I = $ 74.67
Hence, the simple interest accumulated on a principal of $ 700.00 at a rate of 8% per year for 16 months is $ 74.67.
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Homework Progress
28/37 Marks
a) Complete the prime factor trees for 16 and 40:
16
b)
2
2
∞
2
4
2
2
40
2
What is the lowest Common Multiple of 16 and 40?
2
1
5
The prime factor trees for 16 and 40 could be 2,2,2,2 and 2,2,2,5 respectively and and the common multiple of 16 and 40 could be 2 .
What is prime factor ?
prime factor can be defined as the number which is divisible by that number and the number should be prime.
The prime factor tree for 16 as follows
16 = 2*8 = 2* 2 * 4 = 2*2*2*2
16
2 8
2 4
2 2
The prime factor tree for 40 as follows
40 = 2*20 = 2*2*10 = 2*2*2*5
40
2 20
2 10
2 5
Hence, The prime factor trees for 16 and 40 could be 2,2,2,2 and 2,2,2,5 respectively and the common multiple of 16 and 40 could be 2 .
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How many times smaller is 1.2 × 106 than 1.38 × 107?
The number 1.2 × 10⁶ is 11.5 times smaller in comparison to the number 1.38 × 10⁷.
The two given numbers here have been written using the method of powers of 10. In this method, very large or very small numbers are easily simplified and written by denoting the powers of 10. These power are integral in nature. Very large numbers are of the form y × 10ⁿ and very small numbers can be expressed in the form z × 10⁻ⁿ.
In the given problem, we have the numbers 1.2 × 10⁶ and 1.38 × 10⁷ and we have to tell how much the former number is from the latter. For this, we divide the two and easily find our solution. Before this, we have to make the powers of 10 in both numbers the same. We can rewrite the 1.38 × 10⁷ as 13.8 × 10⁶. Now, we divide the two and get-
⇒ 11.5
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Answer: B. 11.5
Step-by-step explanation: I took the test
What is an example of a no solution equation?
The equation 5x + 5 = 5x - 5 has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).
No solution equation:
5x + 5 = 5x - 5
To solve this equation, we must first isolate the variable. To do this, we can subtract 5x from both sides of the equation.
5x + 5 = 5x - 5
Subtract 5x from both sides:
5 + 5 = - 5
Simplify:
10 = -5
At this point, we can see that this equation has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).
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What is the coefficient of y² in the expression 2x²y 10xy² 5y?
The coefficient of yA² for the three given expressions are 2, 10 and 5 respectively.
What is expression?
It is a mathematical statement that defines a mathematical concept as well as the system of a mathematical operation express in a symbolic form.
Mathematical expression is made up of at least two numerical terms along with a sign or at least two terms along with a sign. The expression having two or more numerical terms is called numerical expression.
As example 4 + 3 or 100÷4
The expression which has both variables and numbers is called algebraic expression.
As example X+6 or 25+5y
What is coefficient?
In an expression, the numbers which are accompanied by variables is called coefficient. As example, 24 + 3y, where 3 is the coefficient of y
but 24 is a constant number.
How can we determine the coefficient from the given expression?
We are given three expressions, these are 2xA²y, 10xyA² and 5yA²
for the 1st expression, 2 is the coefficient of A²y
for the 2nd expression, 10 is the coefficient
for the last 5 is the coefficient.
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What does using the if __ name __ == '__ main __' syntax allow programmers to do?
The if __name__ == '__main__' syntax allows a programmer to specify that certain code should only be executed when the script is run directly, rather than when it is imported as a module into another script.
This can be useful for running code that you only want to execute when you're running the script for testing or development, rather than when you're using it as a library in another program. It also allows to use the same code in multiple script without running the main code.
When a Python script is run, the interpreter assigns the name __main__ to the script's global namespace. Therefore, when the script is run directly, __name__ will be set to __main__. When the script is imported as a module into another script, __name__ will be set to the name of the module, rather than __main__.
So, when a programmer uses the if __name__ == '__main__' syntax, they are essentially checking whether the script is being run directly or imported as a module. If the script is being run directly, the code within the if block will be executed. If the script is being imported as a module, the code within the if block will not be executed.
This allows the programmer to separate code that should only be run when the script is executed directly from code that is intended to be used as a library when the script is imported as a module. It also allows to use the same code in multiple script without running the main code.
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6 = x +2y solve for y
What is irrational statement?
An irrational statement is a kind of genuine number that can't be addressed as a basic portion. It can't be communicated in that frame of mind of a proportion. If N is silly, N isn't equivalent to p/q where p and q are numbers and q isn't equivalent to 0. Model: √2, √3, √5, √11, √21, π(Pi) are nonsensical.
A number can't be communicated as a portion of any numbers and. . Unreasonable numbers have decimal developments that neither end nor become occasional. Each supernatural number is irrational.
If a square root is not an ideal square, then it is viewed as an unreasonable number. These numbers can't be composed as a portion because the decimal doesn't end (non-terminating) and doesn't rehash an example (non-repeating).
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Select all the pairs of operations that have inverse relationships.
The pairs of operations that have inverse relationships are subtraction and addition and multiplication and division. The correct options are A and D.
What are algebraic operations?Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, are considered basic algebraic operations in mathematics (fractional power).
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The inverse operations can be subtraction and addition and multiplication and division.
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50 POINTS!!!! urgent!!!!!!
Mary is collecting cup cakes for the school fair. She will make 12 cupcakes to start it off. She plans to collect 24 cupcakes each
day from her surrounding neighborhood for the next 3 days. If you model this word problem for Mary as y=mx+b then match the
corrects pairs.
a. 12
b. 84
c. 3
d. 24
1. m
2. y
3. x
4. b
Since the problem is about linear equation in the form of y = mx + b, initial number represents the value of b = 12, the number of days represents the value of x = 3, the daily collection of cupcakes represent the slope m = 24, then the value of y is:
y = 24*3 + 12 = 72 + 12 = 84So the matching pairs are:
a ⇔ 4, b ⇔ 2,c ⇔ 3,d ⇔ 1 .Complete the equation of the line who’s y intercept is (0,-1) and slope is 4
Y=4x-1
The equation of a line is:
Y=mx+c
We are told that the slope is 4 which is also gradient, meaning that M=4
Now we are left with:
Y=4x+c
There are two ways to get C:
1. We know that C represents the y-intercept so immediately we can conclude that C=-1
2. You can work it out by substituting the coordinate for the X and Y value:
-1=4(0)+c
-1=C
So in conclusion, the equation of the line is:
Y=4x-1
x^5 multiplied by x^3 /x^4
Answer:
x^4
Step-by-step explanation:
[tex]x {}^{5} \times \frac{x {}^{3} }{x {}^{4 \\ } } \\ \\ \frac{ {x}^{8} }{x {}^{4} } \\ \\ x {}^{8 \: - \: 4} \\ {x}^{4} [/tex]
What is the least common multiple of 51, 68 and 85?
Answer:
1020
Step-by-step explanation:
Jayden has been reading a 275275275-page book for English class. On average, he has read about 101010 pages in 151515 minutes (\text{min})(min)(, start text, m, i, n, end text, ). With a deadline looming, Jayden realizes that he won't finish in time unless he skims through the rest of the book. If he skims the book, he can cover 151515 pages in 10\,\text{min}10min10, start text, m, i, n, end text. If it takes Jayden 555 hours and 50\,\text{min}50min50, start text, m, i, n, end text to finish the book (reading and skimming combined), how many pages did Jayden have to skim through
Jayden had to skim through an amount of 75 pages, in the given word problem.
What is word problem?A word problem is a few sentences that describe a "real-life" scenario in which a problem must be solved using a mathematical calculation.
Word problems are regarded as an important part of the primary curriculum because they require children to apply their knowledge of various concepts to'real-life' scenarios.
Let S = no. of skimmed pages
Let R = no. of read pages
Then S + R = 275
So R = 275 - S
Reading rate = 15 min/10 pages
Skimming rate = 10 min/15 pages
Total time to finish book = 350 min
So,
(R)(Reading rate) + (S)(Skimming rate) = 350 minutes
Substituting the values:
(275-S)(15/10) + (S)(10/15)=350
Multiplying equation through by 30 yields:
12375 - 45S + 20S = 10500
Combine terms
1875=25S
S = 75
Thus, Jayden had to skim through an amount of 75 pages.
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Multiply the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x. (8x 3)(4x 7)
The product of the two polynomials is (8x³)(4x⁷) = 32x¹⁰.
THE POLYNOMIALSWhen we multiply two polynomials together, we add the exponents of the x's in each term. In this case, we have 8x³ and 4x⁷. The x in 8x³ has an exponent of 3, and the x in 4x⁷ has an exponent of 7. To find the product of the two polynomials, we add the exponents of the x's in each term, so 3 + 7 = 10. The x in the product will have an exponent of 10. The coefficient, or the number in front of the x, is also multiplied together, so 8 × 4 = 32.So the final answer is 32x¹⁰, where 32 is the coefficient and 10 is the exponent of x.The polynomial 32x¹⁰ is an example of a polynomial, but it's not a characteristic of a polynomial.A polynomial is a mathematical expression involving a sum of powers in one or more variables (such as x, y, z) with non-negative integer exponents and real or complex coefficients. A polynomial can have one or more terms, and each term is separated by a plus or minus sign.Learn more about polynomial here:
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The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
The solution of the system of equations is:
x = 5t - 4
y = -5t + 1
z = t
Option B is the correct answer.
What is a matrix?A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
We have,
From the row-echelon form of the augmented matrix of a system of equations, we get,
x + 0y -5z = -4
x - 5z = -4
x = 5z - 4
0x + y + 5z = 1
y + 5z = 1
y = -5z + 1
0x + 0y + 0z = 0
Now,
Put z = t (any real number)
We get,
x = 5t - 4
y = -5t + 1
Thus,
The solutions are:
x = 5t - 4
y = -5t + 1
z = t
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Help me pls
A small town had a population of 1,260 last year.
Over the course of the past year, the population has
grown by 2 percent. Which function could be used to
model the current population?
P(t) = 1,260(1. 2)
p(t) = 1,260(1. 002)'
P(t) = 1,260(0. 02)'
p(t) = 1,260(1. 02)
The correct option is (d).
The function that could be used to model the current population is P(t) = 1,260(1.02)
This function models the growth of the population over time, t. The base population is 1,260 and the growth factor is 1.02, which represents a 2% increase. The function multiplies the base population by the growth factor to find the new population after one year.
The other options are not correct because:
P(t) = 1,260(1.2) is incorrect because the growth factor is incorrect, it's 1.2 which represents a 20% increase, which is too much compared to the 2% increase mentioned in the problem statement.
p(t) = 1,260(1.002) is incorrect because the growth factor is incorrect, it's 1.002 which represents a 0.2% increase, which is too small compared to the 2% increase mentioned in the problem statement.
P(t) = 1,260(0.02) is incorrect because the growth factor is incorrect, it's 0.02 which represents a 2% increase, but it is not raised to the power of t.
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Construction A construction company is building a new parking garage and is
charging the following rates: $5000 a month for the first 2 months; $8000 a month
for the next 4 months; $6000 in total for the last 4 months, when the garage will be
completed. This amount will be paid in a lump sum at the end of the 6th month.
Express the cost C (in thousands of dollars) as a function of
the time t (in months) that the construction company works
on the parking garage.
Answer:
C(t) = 5t for 0 < t ≤ 3
C(t) = (8t-9) for 3 < t ≤ 6
C(t) = 44 for 6 < t ≤ 10
C is given in thousands of dollars and t is given in months.
Total lump sum to be paid at the end of the 6 months for the total 10 months that the construction company works on the parking garage = $44000
Step-by-step explanation:
We will do a piecewise analysis for this cost function.
How to obtain the total cost changes with each time interval.
In the first 3 months,
C(t) = 5t for 0 < t ≤ 3
Note that C is given in thousands of dollars
In the next 3 months,
C(t) = (8t-9) for 3 < t ≤ 6
- Here, it gets a little complex, we use the upper limit of the previous interval and the lower limit of this new interval to get the constant to be subtracted from the normal 8t that characterizes this interval.
8(3) = 24
5(3) = 15
constant = 24 - 15 = 9
In the last 4 months,
C(t) = 44 for 6 < t ≤ 10
- For the last four months, it is a single sum of $5000 plus the [8(6) - 9] from the previous inteval
C = [8(6) - 9] + 5 = 39 + 5 = 44
So, the cost of parking, tracked month after month gives
T | Cost (in thousands of dollars)
1 | 5
2 | 10
3 | 15
4 | 23
5 | 31
6 | 39
7 | 44
8 | 44
9 | 44
10 | 44
Total lump sum to be paid at the end of the 6 months for the total 10 months that the construction company works on the parking garage = $44000
Hope this Helps!!!
This is not my answer yet is a stollen verrified one.
Raina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges and allows unlimited mileage. Company B has an initial fee of and charges an additional for every mile driven. For what mileages will Company A charge less than Company B
For mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.
To compare the prices of the two companies, we need to determine the total cost for each company at different mileage.
For Company A, the total cost is the initial fee of $50. This is a fixed price, regardless of the mileage driven.
For Company B, the total cost is the initial fee of $30 plus the additional cost per mile driven. To calculate this, we can use the formula:
Total cost = initial fee + (mileage * additional cost per mile)
For Company B, this would be:
Total cost = $30 + (mileage * $0.50)
To find out when Company A charges less than Company B, we need to compare the total costs of the two companies at different mileage. We can set up the following inequality:
$50 <= $30 + (mileage * $0.50)
To solve for mileage, we need to isolate it on one side of the inequality. To do this, we can subtract $30 from both sides:
$20 <= (mileage * $0.50)
Then, we can divide both sides by $0.50:
40 <= mileage
So for mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.
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If the length of the American flag is 1.8 yards, find the hight
What does += mean in Python?
In Python an operator += is an assignment operator which adds the value on its right to the variable and assigns the result to the variable on its left.
We know that an operator is a symbol that represents a mathematical or logical process.
We know that in Python the operator += provides a convenient way to add a value to an existing variable and assign the new value back to the same variable.
If p += q
This means, the variable p the left side is getting added to the value on the right side (q), and the result is then reassigned to the variable on the left.
i.e., p = p + q
+= is an assignment operator.
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Order the set of numbers from least to greatest: 5, -19, -25, 7, 22, -4, -15
Answer:
-25, -19, -15, -4, 5, 7, 22
Step-by-step explanation:
-25, -19, -15, -4, 5, 7, 22 is the order from least to greatest
The bigger the negative number, the smaller it is; that is why the order is
-25, -19, -15, -4, 5, 7, 22
How can you tell if a graph is linear or logarithmic?
A linear graph will have a straight line, whereas a logarithmic graph will have a curved line.
1. Look at the graph and identify the shape of the line.
2. If the line is straight, then the graph is linear.
3. If the line is curved, then the graph is logarithmic.
When looking at a graph, you can tell if it is linear or logarithmic by examining the shape of the line. A linear graph will have a straight line, whereas a logarithmic graph will have a curved line. This is due to the fact that a linear graph is plotted by plotting the points of a linear equation, whereas a logarithmic graph is plotted by plotting the points of a logarithmic equation. The linear equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The logarithmic equation is of the form y = logb(x), where b is the base of the logarithm. Thus, the shape of the line will depend on the form of the equation used to plot the graph. If the line is straight, then it is a linear graph, and if it is curved, then it is a logarithmic graph.
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