Answers
See below for the interpretation of the graph
How to interpret the graph?From the graph, the initial values of x and y are 0
As x increases, y decreases.
This means that the first statement is
Initially, as x increases, y decreases.Slope is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
Using the graph values at the interval x =0 to x = 3, we have:
[tex]m = \frac{-3 - 0}{3 - 0}[/tex]
m = -1
This means that the second statement is
The slope of the graph is equal to -1 for all x between x = 0 and x = 3From the graph, y = -3, when x = 3
As x increases at this point, y increases.
This means that the third statement is
Starting at x = 3, the function value y increases as x increasesUsing the graph values at the interval x = 3 to x = 5, we have:
[tex]m = \frac{3 + 3}{5 - 3}[/tex]
m = 3
This means that the fourth statement is
The slope of the graph is equal to 3 for x between x = 3 and x = 5All y values at x = 0 to x = 4 are less than 0, while all y values at x = 4 to x = 8 are greater than 0
So, the last two statements are
For x between x = 0 and x = 4, the function value y is less than 0For x between x = 4 and x = 8, the function value y is greater than 0Read more about functions at:
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Related Questions
pls help math problem pls
Answers
Answer: The fourth choice
Step-by-step explanation:
(f - g)(x) = f(x) - g(x) = 4[tex]x^{2}[/tex] - 5x - (3[tex]x^{2}[/tex] + 6x - 4) = [tex]x^{2}[/tex] - 11x + 4
X + 2/3 = 8/9 x=? /////////////////////////////////////////
Answers
The value of x is 2/9
Given equation x +2/3 = 8/9
We need to find the value of x
Simplifying the equation is
x+2/3 = 8/9
x = 8/9 -2/3
Taking L.C.M of the denominators 3 and 9
The L.C.M is 9
So we will multiply the numerator and denominator with 1 in 8/9
And we will multiply the numerator and denominator with 3 in 2/3
Hence the new equation formed = 8/9-6/9
Solving this equation we get
8-6 / 9
= 2 / 9
Hence the value of x is 2/9
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Lines b and c are parallel. What is the measure of angle 6
Answers
The measure of ∠6 is 54 degrees.
How to find the angles in a parallel lines?When parallel lines are cut by a transversal, angle relationship are formed. Therefore,
∠6 = 5x + 9 (vertically opposite angles)
∠6 = ∠2
Hence,
∠2 + 13x + 9 = 180
5x + 9 + 13x + 9 = 180
18x = 162
x = 162 / 18
x = 9
Hence,
∠6 = 5(9) + 9 54°
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Which graph represents the solution to x<6?
Answers
The function h(x) is given below.
h(x) = {(3,-5), (5, -7), (6, -9), (10, -12), (12,-16)}
Which of the following gives h¹(x)?
O ((3, 5), (5, 7), (6, 9), (10, 12), (12, 16)}
O ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
O ((3,-5), (5,-7), (6, -9), (10, -12), (12,-16)}
O ((5, 3), (7,5), (9, 6), (12, 10), (16, 12)}
Answers
Answer: Option (2)
Step-by-step explanation:
The inverse of a function swaps the domain and range.
The inverse of the function h(x) is
B. h'(x) = ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
Option B is the correct answer.
We have,
The function h(x) is given as:
h(x) = {(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)}
To find h¹(x) (the inverse of h(x)), we need to swap the x and y values in each ordered pair.
The inverse function will have the y-values of h(x) as the x-values, and the x-values of h(x) as the y-values.
So,
h¹(x) would be:
h¹(x) = {(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
Thus,
The inverse of the function h(x) is
B. h'(x) = ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
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Mr. Krueger wanted a square platform built in the drama room at
school. He provided the carpenter with the desired area of the platform
to be built. Which function can he use to determine the side length of
the square platform?
F(x)=x²
F(x)=√x
F(x) = -=-=
F(x) = |x|
Answers
Explanation: inverse of square is square root. Since the area is the side length squared, take the square root of the area to find the side length.
A line passes through points (2,5) and (6.-7) and has a y-intercept at (0,3). Write the linear equation of this line
Answers
Answer: -9/4.
The slope formula of the line passing through the points
slope and why intercept?
Answers
Answer:
Slope: -1/3
Y-intercept: 0
Step-by-step explanation:
The lines passes the y-axis at 0, and since the line is going downwards, the slope will be negative.
I hope it helps! Have a great day!
bren~
The picnic breakfast cost $12. Jasmine left a tip that was 15 percent of the
cost of the meal. How much money was the tip that Jasmine left?
Answers
0.15 = 15%
PLEASE HELP IM STUCK
Answers
Answer:
The 18th term would be "-70"
Answer:
-70
Step-by-step explanation:
Please look at the picture, I need help ASAP.
Answers
See below for the proof that the areas of the lune and the isosceles triangle are equal
How to prove the areas?The area of the isosceles triangle is:
[tex]A_1 = \frac 12r^2\sin(\theta)[/tex]
Where r represents the radius.
From the figure, we have:
[tex]\theta = 90[/tex]
So, the equation becomes
[tex]A_1 = \frac 12r^2\sin(90)[/tex]
Evaluate
[tex]A_1 = \frac 12r^2[/tex]
Next, we calculate the length (L) of the chord as follows:
[tex]\sin(45) = \frac{\frac 12L}{r}[/tex]
Multiply both sides by r
[tex]r\sin(45) = \frac 12L[/tex]
Multiply by 2
[tex]L = 2r\sin(45)[/tex]
This gives
[tex]L = 2r\times \frac{\sqrt 2}{2}[/tex]
[tex]L = r\sqrt 2[/tex]
The area of the semicircle is then calculated as:
[tex]A_2 = \frac 12 \pi (\frac{L}{2})^2[/tex]
This gives
[tex]A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2[/tex]
Evaluate the square
[tex]A_2 = \frac 12 \pi (\frac{2r^2}{4})[/tex]
Divide
[tex]A_2 = \frac{\pi r^2}{4}[/tex]
Next, calculate the area of the chord using
[tex]A_3 = \frac 12r^2(\theta - \sin(\theta))[/tex]
Recall that:
[tex]\theta = 90[/tex]
Convert to radians
[tex]\theta = \frac{\pi}{2}[/tex]
So, we have:
[tex]A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))[/tex]
This gives
[tex]A_3 = \frac 12r^2(\frac{\pi}{2} - 1)[/tex]
The area of the lune is then calculated as:
[tex]A = A_2 - A_3[/tex]
This gives
[tex]A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)[/tex]
Expand
[tex]A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2[/tex]
Evaluate the difference
[tex]A = \frac 12r^2[/tex]
Recall that the area of the isosceles triangle is
[tex]A_1 = \frac 12r^2[/tex]
By comparison, we have:
[tex]A = A_1 = \frac 12r^2[/tex]
This means that the areas of the lune and the isosceles triangle are equal
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. In your rectangular backyard, you know the width of the yard is three less than four times the length. If the perimeter of your yard is 24 yards, what is the width?
Answers
The width of the rectangular backyard is 9 yards.
How to find the width of the rectangle?The width of the yard is three less than four times the length.
Therefore,
w = 4l - 3
Perimeter of a rectangle = 2l + 2w
where
l = length
w = width
Hence,
24 = 2l + 2(4l - 3)
24 = 2l + 8l - 6
24 = 10l - 6
24 + 6 = 10l
30 = 10l
l = 30 / 10
l = 3 yards
Hence,
w = 4(3) - 3
w = 12 - 3
w = 9 yards
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Consider the volume of the region shown below, which shows a right circular cone with a top radius of 3 cm and height 9cm
Answers
Answer:
84.82 cm
Step-by-step explanation:
Volume of a cone: [tex]\frac{1}{3} \pi r^2h[/tex]
[tex]\frac{1}{3} \pi r^2h\\\\\\\\= \frac{1}{3}\pi (3)^2(9)\\\\= \frac{1}{3}\pi(9)(9)\\\\\\\= \frac{1}{3} \pi (81)\\\\= 27\pi \\[/tex]
≈ 84.82 cm
PLEASE HELP IM SERIOUSLY STUCK ON THIS
Answers
The purchase price of the new car if the sales tax is $3500 is $50000
Direct variationLet the amount of sales tax be A and the purchase price be p
If the amount of sales tax is directly proportional to the purchase price, this is expressed as:
S = kp
If S = $1750 and p = $25000, the;
k = S/p
k = 1750/25000
k = 175/2500
If the sales tax is $3500, the purchase price will be given as:
S = kp
3500 = 175/2500 p
175p = 3500*2500
175p = 8750000
p = 8750000/175
p = 50000
Hence the purchase price of the new car if the sales tax is $3500 is $50000
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The figure shows an example of a multiplication problem where the numbers are coded by letters. Same letter represents same digits, and different letters represent different digits. Which digit does the letter x represent?
Answers
Based on the information provided, it can inferred that letter A is equivalent to 4.
What is the value of letter B?The image shows B + B+ A = A. This is only possible if letter adding 2 letters B is equal to 10. Now 10/2 = 5. This means B = 5.
What is the value of the letter A?It is known 5 + A + A = A. This is only possible is A is 4. 5 + 4+ 4 + 1 (from the previous addition) = 4 (+2 that is added in the next column).
Note: This question is incomplete below I add the missing image.
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use the graph to the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and a scale factor of 10
Answers
The coordinates of QRTW after dilation by factor 10 are (-20,30),(-30,10),(20,-10),(-20,40).
Given that coordinates of QRTW before dilation are (-2,3),(-3,1),(2,-1),(-2,4) and figure QRTW is dilated by factor 10.
We know that if a figure is dilated its area, increases. The new coordinates can be calculated as x*factor from which it is dilated.
Coordinates are the points on the graph surface.
In our figure Q(-2,3), R(-3,1), S(2,-1), T (-2,4).
We have to just multiply each value with 10 to get the new coordinates of QRTW after dilation.
Q after dilation=(-2*10,3*10)=(-20,30)
R after dilation=(-3*10,1*10)=(-30,10)
S after dilation=(2*10,-1*10)=(20,-10)
T after dilation=(-2*10,4*10)=(-20,40)
Hence the vertices of the image QRTW after dilation are (-20,30),(-30,10),(20,-10),(-20,40).
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A rectangular field is to be enclosed by 400m of fencing. Use quadratic to
determine what dimensions will result in the maximum area inside the fence. Show
all your work.
Answers
Work:
First it's a rectangle so its area is equal to the product (multiplication) of both sides of the rectangle (dimensions). A = a x b = ab
NOW: knowing the the circumference or perimeter is equal to 400m, we can say that P = 400 = 2(a+b) = 2a + 2b since the given polynom is rectangle. 2a + 2b = 400 <==> 2a = 400 - 2b <==> a = 200 - b.
We gave an expression of a in function of b. Now we can replace the variable a by 200 - b in the first expression of the area.
A = ab = (200-b)b = 200b-b^2 = -b^2 + 200b
A is now a quadratic equation. We note A(b) the epression -b^2 +200b so:
A(b) = -b^2 +200b
We can already see that A is a quadratic equation of the form:
ax^2 + b + c. The a coefficient is negative which will lead to closed parabola when looking from the top. Now we need to find the maximum of the function by using the derivatives:
A(b) = -b^2 +200b <==> A'(b) = -2b + 200b
and -2b + 200b = 0 <==> b = 100;
So the derivative function crosses the x-axis at (100; 0).
So is increasing over ]-∞; 100] and decreasing over [100; ∞[.
We obtain a maxima on (100; x) with A. To find it we need to replace 100 by b in the function A.
A(b) = -b^2 + 200b
<==> A(100) = -100^2 + 200 x 100 = - 10000 + 20000 = 10000
Now let's find a: if b = 100 what equals a ?
We know that ab = 10000 <==> 100a = 10000 <==> a = 100;
And we verify that ab = 100 x 100 = 10000.
The rectangle needs to be a square to reach the maximum area of 10000m^2 or also 0.01 km^2.
Q.E.D.
PLEASE HELP WILL GIVE YOU ALL MY POINTS In the picture, t || s, mz1 = 10x + 2, and mz2 = 12x - 22. Find the measure of angle 2.
Answers
Answer:
[tex]\huge\boxed{\sf < 2 = 122\°}[/tex]
Step-by-step explanation:
From the figure,
∠1 = ∠2 (Alternate angles are equal)We know that:
∠1 = 10x + 2∠2 = 12x - 22So,
10x + 2 = 12x - 22Add 22 to both sides
10x + 2 + 22 = 12x
10x + 24 = 12x
Subtract 10x to both sides
24 = 12x - 10x
24 = 2x
Divide 2 to both sides
12 = x
OR
x = 12Given that,
∠2 = 12x - 22
Put x = 12
∠2 = 12(12) - 22
∠2 = 144 - 22
∠2 = 122°[tex]\rule[225]{225}{2}[/tex]
Answer: 122°
Step-by-step explanation:
∠1 an ∠2 are alternate interior angles, which are angles that are inside both parentheses and are on alternate sides of the transversal. The Alternate Interior Angles Theorem states that if two lines are parallel and cut by a transversal, then the alternate interior angles formed are congruent.
Since the lines are parallel as given in the question, ∠1 and ∠2 are of equal measure. We can solve for ∠2 by first solving for x, then plugging it in ∠2's measure.
[tex]10x+2=12x-22[/tex]
[tex]-2x=-24[/tex]
[tex]x=12[/tex]
Putting x in the expression 12x-22, we get
[tex]12(12)-22\\144-22\\122[/tex]
Hence, the value of ∠2 is 122°.
Given that f(x) = -6x and g(x) = x + 4, multiply the functions (f •g)(x).
Answers
Answer:
(f • g)(x) = -6x² - 24x
Step-by-step explanation:
The expression (f • g)(x) can be written in an expanded form, f(x) • g(x).
(f • g)(x) <----- Original expression
f(x) • g(x) <----- Rewritten expression
(- 6 x) • (x + 4) <----- Insert functions
-6x² - 24x <----- Multiply -6x and x, and multiply -6x and 4
Round 5 358 708 to the nearest million
Answers
Answer:5 million
Step-by-step explanation: Because 300 thousand is below 500 thousand so if its below 500 thousand it cant round up it rounds down.
Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below. In this function, Po is the air pressure at the surface of the Earth, and h is the height above the surface of the Earth, measured in meters. Which expression best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth
Answers
The expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.
Air pressure at an altitude above the surface of the EarthThe air pressure at an altitude of 3,000 meters above the surface of the Earth is calculated as follows;
Po = ρgh
where;
ρ is density of airg is acceleration due to gravityh is the altitudeSubstitute the value of altitude into the equation;
Po = 3,000ρg
Thus, the expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.
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Please help me on this geometry question
Answers
Answer:
? = 3
Step-by-step explanation:
given a line parallel to a side of the triangle and intersecting the other 2 sides, then it divides those sides proportionally , that is
[tex]\frac{?}{6}[/tex] = [tex]\frac{2}{4}[/tex] ( cross- multiply )
4? = 12 ( divide both sides by 4 )
? = 3
Answer:
3
Step-by-step explanation:
Because the triangles are similar
6/4 = (?+6)/(2+4)
6/4 = (?+6)/6
Cross multiply
36 = 4?+24
4?=12
?=3
The volume of a solid revolution generated by rotating the curve y = f(x) and x = f(y) between x = a and x = b , y = a and y = b through 360 degrees about the x-axis and y-axis is given
[tex]V_{x} =\int\limits^b_a {\pi y^{2} } \, dx[/tex] and [tex]V_{y} =\int\limits^b_a {\pi x^{2} } \, dy[/tex]
The diagram shows the line y = 1, the line y = 4 and part of the curve [tex]y=3x^2[/tex]. The shaded region is rotated through 360 degrees about the y-axis. Find the exact value of the volume of revolution obtained. Leave your answer in pi.
Answers
Answer:
[tex]\dfrac{5}{2}\pi[/tex]
Step-by-step explanation:
Rotation about the y-axis
[tex]\textsf{Volume}=\displaystyle \int^b_a \pi x^2\:\text{d}y[/tex]
where:
b = upper limita = lower limitx is a function of yGiven function of y: [tex]y = 3x^2[/tex]
Rewrite the given function as a function of y:
[tex]\implies x^2=\dfrac{1}{3}y[/tex]
Substitute the values into the formula:
[tex]\implies \displaystyle \int^4_1 \dfrac{1}{3}\pi y\:\:\text{d}y[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ay^n\:\text{d}y=a \int y^n \:\text{d}y$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $y^n$}\\\\$\displaystyle \int y^n\:\text{d}y=\dfrac{y^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
Take out the constant and integrate:
[tex]\begin{aligned}\implies \dfrac{1}{3}\pi\displaystyle \int^4_1 y\:\:\text{d}y & = \dfrac{1}{3}\pi \left[\dfrac{1}{2}y^2\right]^4_1\\\\& =\dfrac{1}{3}\pi \left[\dfrac{1}{2}(4)^2-\dfrac{1}{2}(1)^2\right]\\\\&=\dfrac{1}{3}\pi\left[8-\dfrac{1}{2}\right]\\\\&=\dfrac{5}{2}\pi \end{aligned}[/tex]
Therefore, the exact value of the volume of revolution is:
[tex]\dfrac{5}{2}\pi[/tex]
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Find the area of a circle with radius, r =
7.4m.
Give your answer rounded to 2 DP.
r
C
The diagram is not drawn to scale.
Answers
Answer:
172.03 m²
Step-by-step explanation:
Hello!
Area of a circle: [tex]A = \pi r^2[/tex]
A = areaπ = pir = radiusPlug in the radius into the formula to find the area.
Find the Area[tex]A = \pi r^2[/tex][tex]A = \pi (7.4)^2[/tex][tex]A = 54.76\pi[/tex][tex]A = 172.0336137106 \approx 172.03[/tex]The area is approximately 172.03 m².
To calculate the radius of this circle, we must take into account that:
Data:
R = 7.4 π = 3.14To calculate the area of the circle, we apply the following formula:
A = π * r², wherea = area
π = pi
r = radius
Substituting the values of the equation:
[tex]\large\displaystyle\text{$\begin{gathered}\sf A=3.14*(7.4 \ m)^{2} \end{gathered}$}[/tex]Taking the square root
[tex]\large\displaystyle\text{$\begin{gathered}\sf A=3.14*54.76 \ m^{2} \end{gathered}$}[/tex]Multiplying
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf A=171.95 \ m^{2} \end{gathered}$}}[/tex]Answer: The approximate area of the circle is 171.95 m².
Instructions: Given the coordinates, Complete the translation (x,y)→(x+2,y−2) C(−5,−1) D(−4,3) E(−3,2) F(−2,0)
Answers
the translations is,
C(-5,-1) → (-3,-3)
D(-4,3) → (-2,1)
E(-3,2) → (-1,0)
F(-2,0) → (0,-2)
What is Translation ?
The changes in the value of the x and y coordinates is known as translation.
Calculation:
The given points are C(-5,-1), E(-4,3), F(-3,2), F(-2,0).
according to the question (x,y)→(x+2,y-2)
this means x coordinate changes by addition of 2
And the y coordinate changes by subtraction of 2
Addition and Subtraction in the Coordinates,
C(-5,-1) → (-5+2,-1-2) → (-3,-3)
D(-4,3) → (-4+2,3-2) → (-2,1)
E(-3,2) → (-3+2,2-2) → (-1,0)
F(-2,0) → (-2+2,0-2) → (0,-2)
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Given that DRWH is a parallelogram, determine the values of x and y.
Answers
Answer:
the opposite sides of the parallelogram are equal.
so DR = HW mean : 2 y + 2 = 3 y - 9
3y - 2y = 9+2
y = 11
RW = y+4 = 11+4 = 15
DH = RW
so, 3 x + 6 = 15
3x = 15-6 = 9
x = 3
Δ
X
Y
Z
and
Δ
A
B
C
are similar triangles. Given the dimensions shown in the diagram, what is the area of
Δ
A
B
C
? Express the answer in square units.
Answers
Answer:
3.528
Step-by-step explanation:
the scale factor from the large triangle to the smaller triangle is 1/2. All of the side lengths of the small triangle is 1/2 the side lengths of the large triangle.
A = 1/2 (bh) The area of a triangle. I need to know the base and the height of the little triangle to figure out the area. If I use AC as the base, the length is given to me. It is 4.2. I do not have the height of the base, but I know that it is half of the height of the large triangle and that number is given to me. It is 3.36, if I divide that by 2, I get 1.68. Now I know all that I need to find the area.
A = 1/2(4.2)(1.68)
3.528Units^2
A rectangle has a width of 2.45 feet and a length of 6.5 feet. how will the area of the rectangle change if each side is increased by a factor of 5? the area will be one-fifth the original. the area will be startfraction 1 over 25 endfraction the original. the area will be 25 times the original. the area will be 5 times the original.
Answers
The area of the new rectangle will be 25 times that of the original
Area of a rectangleA rectangle is a 2D shape that has 4 sides and equal interior angles
If rectangle has a width of 2.45 feet and a length of 6.5 feet, then;
Width = 2.45 feet
Length = 6.5feet
A = 2.45 * 6.5
A = 15.925 square feet
If each side of the rectangle is increased by a factor of 5, hence;
W1 = 5(2.45) = 12.25feet
L1 = 5(6.5) = 32.5 feet
Determine the area of the new rectangle
A = 12.25 * 32.5
A = 398.125 square feet
Ratio of the area
A1/A = 398.125/15.925
A1 = 25A
Hence the area of the new rectangle will be 25 times that of the original
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Drag each tile to the correct box.
Each function is a transformation of the parent sine function. Based on the period, which graph represents each transformed function?
Answers
The first graph represents sin(2x), the second graph represents sin(-x) and the third graph represents sin(x/2) .
There are some rules for transformation of graph of various functions which are as follows :-
For F(x) →f(−x) = Reflection about the y-axisFor F(x) → f(ax) = It will depend upon value of a chosenIf |a|>1 then f(ax) is f(x) squashed horizontally by a factor of aIf 0<|a|<1 then f(ax) is f(x) is stretched horizontally by factor of aIf a<0 then is f(ax) is f(x) also reflected in the y-axisBy keeping in mind these rules it is easily observable that the first graph is sinx squashed horizontally by a factor of 2 while second graph is reflection of sinx about the y-axis and the third graph is sinx horizontally stretched by a factor of 2.
Thus the first graph represents sin(2x), the second graph represents
sin(-x) and the third graph represents sin(x/2)
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find the domain and range of f^-1 where f(x)=x+1/6x+7
Answers
Answer:
Step-by-step explanation:
hello here is an solution
The domain and range are (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x)=(x+1)/6x+7
Let f(x)=y
(x+1)/6x+7=y
x+1=y(6x+7)
x+1=6xy+7y
6xy-x=7y-1
x(6y-1)=7y-1
Divide both sides by 6y-1
x=7y-1/6y-1
So f⁻¹(x)=1-7x/6x-1
The domain is (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6}
The range is (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6}
Hence, the domain and range are (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.
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