Quiz about Rational Functions and Transformations of Functions

Question 1

How is this function transformed from the parent function?

Accepted Answer

Translated right and down

Answer

Translated left and up

Answer

Translated right and up

Answer

Translated left and down

Question 2

What is the horizontal asymptote?

Accepted Answer

y = 7

Answer

x = 2

Answer

x = 7

Answer

y = 2

Question 3

What is the horizontal asymptote of the function given?

Accepted Answer

y = 2

Answer

x = 1

Answer

x = 2

Answer

y = -1

Question 4

What are the asymptotes?

g(x) = 4 / (x - 5)

Accepted Answer

x = 5 & y = 0

Answer

x = 5

Answer

x = -5 & y = 4

Answer

None

Question 5

What are the asymptotes?

Accepted Answer

x=-3, y=1

Answer

x=3, y =1

Answer

x=-3, y =-1

Answer

x=3 y=-1

Question 6

What is the vertical asymptote?

Accepted Answer

x = 2

Answer

x = 7

Answer

y = 2

Answer

y = 7

Question 7

What is the horizontal asymptote?

Accepted Answer

y = 7

Answer

x = 2

Answer

x = 7

Answer

y = 2

Question 8

Describe all transformations from the parent function g(x)=1/x to f(x).

Accepted Answer

Shift left 5 and shift up 7

Answer

Shift right 5 and shift up 7

Answer

Shift left 7 and shift up 5

Answer

Reflect over the x-axis, shift up 7

Question 9

What would be the denominator of the function?

Accepted Answer

x-2

Answer

x+2

Answer

x+1

Answer

x-1

Question 10

Describe the transformation of y = f(x) for the new function
y = 1/5f(x)

Accepted Answer

The graph of y = f(x) was compressed vertically by a factor of 1/5

Answer

The graph of y = f(x) compressed horizontally by a factor of 1/5

Answer

The graph of y = f(x) was stretched horizontally by a factor of 5

Answer

The graph of y = f(x) was stretched vertically by a factor of 5

Question 11

Describe the transformation of y = f(x) for the new function

y = - f(x)

Accepted Answer

The graph of y = f(x) was reflected across the x axis.

Answer

The graph of y = f(x) was reflected across the y axis.

Answer

The graph of y = f(x) was translated down.

Answer

The graph of y = f(x) was translated up

Question 12

Describe the transformation of y = g(x) for the function

y = 3g(x - 3) + 5

Accepted Answer

Translated up 5 units

Translated right 3 units

Stretched vertically by a factor of 3

Answer

Translated up 5 units

Translated left 3 units

Stretched vertically by a factor of 3

Answer

Translated down 5 units

Translated left 3 units

Stretched vertically by a factor of 3

Answer

Translated down 5 units

Translated left 3 units

Stretched vertically by a factor of 1/3

Question 13

Which equation describes the transformation of shifting f(x)=x³ seven units up?

Accepted Answer

x3+7

Answer

x3-7

Answer

(x-7)3

Answer

(x+7)3

Question 14

Which equation describes the transformation of shifting f(x)=x³ three units left?

Accepted Answer

(x + 3)3

Answer

x3 + 3

Answer

x3 - 3

Answer

(x - 3)3

Question 15

what is the equation that best matches the graph?

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 16

What is the horizontal asymptote to this function?

Accepted Answer

y=4

Answer

y=0

Answer

y=-2

Answer

y=1

Question 17

What is the horizontal asymptote of this function?

Accepted Answer

y=1/2

Answer

y=2

Answer

x=1/2

Answer

y=1

Question 18

What is the equation of the rational function graphed?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 19

Find the y-intercept.

Accepted Answer

(0, 2)

Answer

(0, -2)

Answer

(0, 4)

Answer

it is undefined

Question 20

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

Accepted Answer

-f(x)

Answer

f(-x)

Answer

f-1(x)

Answer

f(2x)

Question 21

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

Accepted Answer

g(x)=(x-1)³

Answer

g(x)=x3+1

Answer

g(x)=x3-1

Answer

g(x)=(x+1)³

Question 22

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

Accepted Answer

g(x)=2f(x)

Answer

g(x)=0.5f(x)

Answer

g(x)=f(x) + 2

Answer

g(x)=f(x + 2)

Question 23

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

Accepted Answer

(-6, 5)

Answer

(-2, 5)

Answer

(-4, 3)

Answer

(-4, 7)

Rational Functions and Transformations of Functions

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