Lesson on Transformations of Functions

​Functions and Transformations

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Multiple Choice

Which parent function matches the graph? #1

• y = |x|

• y = x

• y = x²

• y = 2^x

Multiple Choice

Which equation below is a quadratic function translated left 4 units? #8

• y = x² + 4

• y = (x + 4)²

• y = (x - 4)²

• y = 4x²

Multiple Choice

Which equation is a quadratic function reflected over the x-axis and shifted up 2? #9

• y = x² + 2

• y = -x² + 2

• y = x² - 2

• y = -(x + 2)²

Multiple Choice

Where is the vertex of $$y=3\left(x-26\right)^2+14$$  ? #30

• (26, 14)

• (14, 26)

• (-26, 14)

• (3, 14)

• (3, 26)

Multiple Choice

Tell how the graph transformed. #12

y = (x - 3)²

• Translated right 3

• Translated left 3

• Translated up 3

• Translated down 9

Multiple Choice

Describe the transformation. #10

• left 2 up 5

• right 2 up 5

• left 2 down 5

• right 2 down 5

Multiple Choice

Given $$f\left(x\right)=2x^2-1$$  , find $$f\left(3\right)$$  . #21

• 17

• 5

• 35

• 25

Multiple Choice

$$Given\ h\left(x\right)=3x^2-2x+8\ what\ is\ h\left(-1\right)?$$  #35

• 13

• 8

• 16

• none of these

Multiple Choice

What type of function is shown? #3

• linear

• quadratic

• square root

• absolute value

Multiple Choice

Which equation is an absolute value graph shifted right 5 units? #11

• y = |x - 5|

• y = |x + 5|

• y = |x| + 5

• y = -5|x|

Multiple Choice

What is the equation for this graph? #14

• f(x)= Ix+2I +1

• f(x)= Ix-2I +1

• f(x)= Ix+2I -1

• f(x)= Ix-2I -1

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Multiple Choice

Describe the transformation that is applied to the parent function.  f(x) =  3 Ix+8I #22

• Stretches by 3, Shifts left 8

• Stretches by 3, Shifts right 8

• Stretches by 3, Shifts up 8

• Stretches by 3, Shifts down 8

Multiple Choice

What is the equation for this function? #24

• $$f\left(x\right)\ =2\left|x-3\right|+2$$

• $$f\left(x\right)\ =\ 2\left|x-3\right|-2$$

• $$f\left(x\right)\ =\ \frac{1}{2}\left|x+3\right|+2$$

• $$f\left(x\right)\ =\ \left|x-3\right|\ -2$$

Multiple Choice

Describe the transformation of the equation below from the absolute value parent function. $$y=-2\left|x-3\right|+3$$  #29

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

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

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

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

Multiple Choice

What type of function is shown? #2

• absolute value

• quadratic

• linear

• exponential

Multiple Choice

How did the equation shift from the parent function? y = f(x - 4) #17

• Shift right by 4

• Shift left by 4

• Horizontal Stretch by 4

• Vertical Stretch by 4

• Shift down by 4

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Multiple Choice

What type of function is shown? #7

• cube root

• square root

• logarithm

• exponential

Multiple Choice

Describe the transformation. #13

• up 3

• down 3

• left 3

• right 3

Multiple Select

Which transformations are involved in the equation $$y=\frac{1}{2}\sqrt{x+1}-1$$  ? #31

• Horizontal translation left

• Vertical shrink

• Vertical translation down

• Horizontal translation right

• Vertical stretch