Quiz about Parent Functions, Key Features, Transformations, Composition

Question 1

What is the parent function for an absolute value function?

Accepted Answer

f(x)=IxI

Answer

f(x)=x3

Answer

f(x)=x

Answer

f(x)=x2

Question 2

What is the parent function for a cubic function?

Accepted Answer

f(x)=x3

Answer

f(x)=x

Answer

f(x)=IxI

Answer

f(x)=x2

Question 3

Describe the transformation that is applied to the parent function.
f(x) = IxI -5

Accepted Answer

Shifts down 5

Answer

Shifts left 5

Answer

Shifts right 5

Answer

Shifts up 5

Question 4

Describe the transformation that is applied to the parent function.
f(x) = 3 Ix+8I

Accepted Answer

Stretches by 3, Shifts left 8

Answer

Stretches by 3, Shifts right 8

Answer

Stretches by 3, Shifts up 8

Answer

Stretches by 3, Shifts down 8

Question 5

Describe the transformation that is applied to the parent function.
f(x) = (1/2) Ix-1I -1

Accepted Answer

Compresses by (1/2), Shifts right 1, down 1

Answer

Compresses by (1/2), Shifts left 1, down 1

Answer

Compresses by (1/2), Shifts left 1, up 1

Answer

Compresses by (1/2), Shifts right 1, up 1

Question 6

Dale graphed the absolute value parent function. Then,he reflected the graph over the x-axis, shifted it four units to the right and three units up. What is the new equation?

Accepted Answer

f(x) = -Ix-4I +3

Answer

f(x) = Ix+4I +3

Answer

f(x) = Ix+4I -3

Answer

f(x) = -Ix+3I +4

Question 7

What is the equation to this graph?

Accepted Answer

f(x)= Ix+2I +1

Answer

f(x)= Ix-2I +1

Answer

f(x)= Ix+2I -1

Answer

f(x)= Ix-2I -1

Question 8

Which parent function matches the graph?

Accepted Answer

y = x2

Answer

y = |x|

Answer

y = x

Answer

y = 2x

Question 9

What type of function is shown?

Accepted Answer

linear

Answer

absolute value

Answer

quadratic

Answer

exponential

Question 10

What is the parent function for an absolute value function?

Accepted Answer

f(x)=IxI

Answer

f(x)=x3

Answer

f(x)=x

Answer

f(x)=x2

Question 11

Given the function $$y=\left(x+4\right)^2+2$$ , what is the parent function?

Accepted Answer

Answer

$$y=a\left(x-h\right)^2+k$$

Answer

Answer

$$y=0\left(x-0\right)^2+0$$

Question 12

$$y=\sqrt{x-\frac{3}{2}}+2$$ belongs to what family of functions?

Accepted Answer

square root

Answer

absolute value

Answer

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Answer

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Question 13

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

Accepted Answer

$$y=-\left|x-15\right|-3$$

Answer

$$y=-\left|x+15\right|-3$$

Answer

$$y=\frac{1}{2}\left|x+3\right|-15$$

Answer

$$y=\frac{1}{2}\left|x-3\right|-15$$

Answer

$$y=\left|-x-15\right|-3$$

Question 14

Which transformations are involved in the equation $$y=\frac{1}{2}\sqrt{x+1}-1$$ ?

Accepted Answer

Vertical shrink

Accepted Answer

Horizontal translation left

Accepted Answer

Vertical translation down

Answer

Horizontal translation right

Answer

Vertical stretch

Question 15

If $$f\left(x\right)=a\left(x-h\right)^2+k$$ has a horiz. shift of -2, a vertical shift of +3 and a vertical stretch of 4, what are the values of a, h, and k?

Accepted Answer

$$a=4;\ h=-2;\ k=3$$

Answer

$$a=2;\ h=4;\ k=-3$$

Answer

$$a=4;\ h=2;\ k=3$$

Answer

$$a=3;\ h=2;\ k=-4$$

Question 16

If $$f\left(x\right)=a\left(x-h\right)^2+k$$ has a horiz. shift of -2, a vert. shift of 3 and a vert. stretch of 4, what is the equation for $$f\left(x\right)$$ ?

Accepted Answer

$$f\left(x\right)=4\left(x+2\right)^2+3$$

Answer

$$f\left(x\right)=4\left(x-2\right)^2+3$$

Answer

$$f\left(x\right)=3\left(x+2\right)^2+4$$

Answer

$$f\left(x\right)=2\left(x-4\right)^2+3$$

Question 17

What does the transformation $$f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9$$ do to the graph of $$f\left(x\right)$$ ?

Accepted Answer

translates it left one unit and down 9 units

Answer

translates it right one unit and down 9 units

Answer

translates it up one unit and right 9 units

Answer

translates it down one unit and left 9 units

Question 18

What does the transformation $$f\left(x\right)\ \rightarrow\ \frac{1}{3}f\left(x\right)+4$$ do to the graph of $$f\left(x\right)$$ ?

Accepted Answer

Shrinks the graph vertically by a factor of 1/3 and translates up 4 units.

Answer

Stretches the graph by a factor of 3 and translates up 4 units.

Answer

Translates the graph left 1/3 of a unit and up 4 units.

Answer

Translates the graph right 3 unites and down 4 units.

Question 19

What type of function is shown?

Accepted Answer

absolute value

Answer

linear

Answer

quadratic

Answer

square root

Question 20

Name the parent function.

Accepted Answer

absolute value

Answer

constant

Answer

square root

Answer

linear

Question 21

Which equation below is a quadratic function translated up 5 units?

Accepted Answer

y = x² + 5

Answer

y = (x + 5)²

Answer

y = 5x2

Answer

y = -x² - 5

Question 22

Which equation below is a quadratic function translated left 4 units?

Accepted Answer

y = (x + 4)²

Answer

y = x² + 4

Answer

y = (x - 4)²

Answer

y = 4x2

Question 23

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

Accepted Answer

y = -x² + 2

Answer

y = x² + 2

Answer

y = x² - 2

Answer

y = -(x + 2)²

Question 24

Which equation is an absolute value graph shifted right 5 units?

Accepted Answer

y = |x - 5|

Answer

y = |x + 5|

Answer

y = |x| + 5

Answer

y = -5|x|

Question 25

Tell how the graph transformed.
y = (x - 3)²

Accepted Answer

Translated right 3

Answer

Translated left 3

Answer

Translated up 3

Answer

Translated down 9

Question 26

Name the parent function.

Accepted Answer

linear

Answer

constant

Answer

quadratic

Answer

exponential

Question 27

Name the parent function.

Accepted Answer

quadratic

Answer

cubic

Answer

square root

Answer

logarithmic

Question 28

Tell how the function transformed from y =x²
y = -2x²

Accepted Answer

Stretched vertically and reflected over x-axis

Answer

Translated left 2 units

Answer

Reflected over x-axis

Answer

Compressed vertically and reflected over the x-axis

Question 29

Question 29.

Accepted Answer

horizontal shift to the right 4 and vertical shift down 2

Answer

horizontal shift to the left 4 and vertical shift down 2

Answer

horizontal shift to the right 4 and vertical shift up 2

Answer

horizontal shift to the left 4 and vertical shift up 2

Question 30

Question 30.

Accepted Answer

horizontal shift to the left 4 and vertical shift down 2

Answer

horizontal shift to the right 4 and vertical shift down 2

Answer

horizontal shift to the left 4 and vertical shift up 2

Answer

horizontal shift to the right 4 and vertical shift up 2

Question 31

Question 31.

Accepted Answer

horizontal shift to the right 2 and vertical shift down 4

Answer

horizontal shift to the right 2 and vertical shift up 4

Answer

horizontal shift to the left 2 and vertical shift up 2

Answer

horizontal shift to the left 2 and vertical shift down 2

Question 32

Question 32.

Accepted Answer

horizontal shift to the right 2 and vertical stretch by a factor of 3

Answer

horizontal shift to the left 2 and vertical stretch by a factor of 3

Answer

horizontal shift to the right 2 and vertical compression by a factor of 3

Answer

horizontal shift to the left 2 and vertical compression by a factor of 3

Question 33

Name the parent function.

Accepted Answer

cubic

Answer

linear

Answer

quadratic

Answer

cube root

Question 34

Name the parent function.

Accepted Answer

exponential

Answer

linear

Answer

logarithmic

Answer

cubic

Question 35

Name the parent function.

Accepted Answer

exponential

Answer

square root

Answer

quadratic

Answer

cubic

Question 36

Name the parent function.

Accepted Answer

cubic

Answer

cube root

Answer

exponential

Answer

quadratic

Question 37

Which equation below is a quadratic function translated up 5 units?

Accepted Answer

y = x² + 5

Answer

y = (x + 5)²

Answer

y = 5x2

Answer

y = -x² - 5

Question 38

Which equation below is a quadratic function translated left 4 units?

Accepted Answer

y = (x + 4)²

Answer

y = x² + 4

Answer

y = (x - 4)²

Answer

y = 4x2

Question 39

Tell how the graph transformed.
y = (x - 3)²

Accepted Answer

Translated right 3

Answer

Translated left 3

Answer

Translated up 3

Answer

Translated down 9

Question 40

Which equation below is a quadratic function translated up 5 units?

Accepted Answer

y = x² + 5

Answer

y = (x + 5)²

Answer

y = 5x2

Answer

y = -x² - 5

Question 41

Which equation below is a quadratic function translated left 4 units?

Accepted Answer

y = (x + 4)²

Answer

y = x² + 4

Answer

y = (x - 4)²

Answer

y = 4x2

Question 42

Describe the transformation

Accepted Answer

right 2 up 5

Answer

left 2 up 5

Answer

left 2 down 5

Answer

right 2 down 5

Question 43

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

Accepted Answer

y = -x² + 2

Answer

y = x² + 2

Answer

y = x² - 2

Answer

y = -(x + 2)²

Question 44

Which equation is an absolute value graph shifted right 5 units?

Accepted Answer

y = |x - 5|

Answer

y = |x + 5|

Answer

y = |x| + 5

Answer

y = -5|x|

Question 45

Question 45.

Accepted Answer

y = -Ix + 2I - 1

Answer

y = Ix + 2I - 1

Answer

y = -Ix - 2I - 1

Answer

y = -Ix + 1I - 2

Question 46

Describe the transformation from the parent graph

Accepted Answer

Reflect over x, right 3, down 4

Answer

Reflect over y, right 3, down 4

Answer

Reflect over x, right 3, up 4

Answer

Reflect over y, left 3, down 4

Question 47

Match the equation with the graph:

Accepted Answer

y = -(x - 2)² + 4

Answer

y = (x - 2)² + 4

Answer

y = -(x - 4)² + 2

Answer

y = -(x + 2)² + 4

Question 48

What shifts have occurred?

Accepted Answer

right 1, up 5

Answer

left 1, up 5

Answer

left 1, down 5

Answer

right 1, down 5

Question 49

Describe the parent graph transformation

Accepted Answer

compression by 1/2, left 1, down 3

Answer

stretch by 1/2, left 1, down 3

Answer

stretch by 1/2, right 1, down 3

Answer

compression by 1/2, right 1, down 3

Question 50

What is the equation of the PARENT  function?

Accepted Answer

f(x) = x3

Answer

f(x) = 2x

Answer

f(x) = |x|

Answer

f(x) = x

Question 51

Which transformation will occur if f(x) = x is replaced with f(x) + 2?

Accepted Answer

Vertical translation up by 2 units.

Answer

Translation left 2 units

Answer

Translation right 2 units

Answer

Reflection across the x-axis.

Question 52

Which transformation on

f(x) = x

is g(x) = -f(x)

Accepted Answer

Reflection across the x-axis.

Answer

Reflection across the y-axis

Answer

The slope will be less steep

Answer

The graph will be wider

Question 53

Which equation transforms f(x) = x to a horizontal stretch by a factor of 2, a reflection over the x axis, and a shift down 4?

Accepted Answer

-f(1/2x) - 4

Answer

f(-2x - 4)

Answer

f(-1/2x) - 4

Answer

-f(2x) - 4

Question 54

Describe the transformation of y = (x - 4)²

Accepted Answer

Shift RIGHT

Answer

Shift UP

Answer

Shift DOWN

Answer

Shift LEFT

Question 55

If the blue is f(x)=x^2,the red must be

Accepted Answer

g(x)=(x-3)²

Answer

g(x)=(x+3)²

Answer

g(x)=x2+3

Answer

g(x)=x2-2

Question 56

Which of the following is the correct equation for the given graph?

Accepted Answer

f(x) = (x + 2)² - 1

Answer

f(x) = (x - 2)² - 1

Answer

f(x) = -(x + 2)² - 1

Answer

f(x) = -(x - 2)² - 1

Question 57

Which of the following is the correct equation for the given graph?

Accepted Answer

f(x) = -3(x - 2)² - 4

Answer

f(x) = -(x + 2)² - 4

Answer

f(x) = -(x - 2)² - 4

Answer

f(x) = -3(x + 2)² - 4

Question 58

What is the equation of the graph below?

Accepted Answer

f(x) = I x - 2 I

Answer

f(x) = I x + 2 I

Answer

f(x) = I x + 2 I +2

Answer

f(x) = I x - 2 I +2

Question 59

What is the equation of the graph below?

Accepted Answer

f(x ) = -I x + 4 I + 2

Answer

f(x ) = I x + 4 I + 2

Answer

f(x ) = -I x - 4 I + 2

Answer

f(x ) = I x - 4 I + 2

Question 60

Write an absolute value function given the following transformations:
Reflection across the x-axis
Vertical shift right 2 units
Horizontal shift down 7 units

Accepted Answer

y = -|x - 2| - 7

Answer

y = -|x + 2| - 7

Answer

y = |x - 2| - 7

Answer

y = -|x - 2| + 7

Question 61

The graph shows the function f(x)=x³ in blue and another function g(x) in red. Which could be the equation for g(x)?

Accepted Answer

D. g(x) = (x - 1)³

Answer

A. g(x) = -x³

Answer

B. g(x) = x³ - 1

Answer

C. g(x) = (x + 1)³

Question 62

Describe the transformation of the graph
y = -(x - 4)³ + 5

Accepted Answer

Reflect x-axis, Right 4, Up 5

Answer

Up 5 and Left 4

Answer

Reflect x-axis, Left 4, Up 5

Answer

Right 4 and up 5

Question 63

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

Accepted Answer

reflected over x axis, stretched by 2, right 3, up 3

Answer

reflected over x axis, stretched by 2, left 3 up 3.

Answer

reflected over x axis, shrunk by 2, right 3, up 3

Answer

reflected over the x axis, shrunk by 2, left 3, up 3

Question 64

Describe the transformation of the equation below from the parent function of y = I x I
y = I x - 4 I

Accepted Answer

Right 4

Answer

Left 4

Answer

Up 4

Answer

Down 4

Parent Functions, Key Features, Transformations, Composition

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