Linear Transformations Translation

Multiple Choice

Describe the transformations from f(x)=x²

f(x)=(x+7)²

• horizontal shift left 7 units

• horizontal shift right 7 units

• vertical shift up 7 units

• vertical shift down 7 units

Multiple Choice

Describe the transformations from f(x)=x²

f(x) = (x-3)² + 5.  

• Left 3 and up 5

• Right 3 and down 5

• Left 3 and down 5

• Right 3 and up 5

Multiple Choice

Which equation describes the transformation of

shifting f(x)=x² two units right?

• x² + 2

• x² - 2

• (x + 2)²

• (x - 2)²

Multiple Choice

Vertical stretch is af(x) when...

• a is greater than 0

• a is less than 0

• a is greater than 1

• a is a fraction/decimal

Multiple Choice

Vertical compression is af(x) when a is...

• a fraction/decimal and the graph flattens

• a number greater than 1 and the graph becomes steeper

• any type of number 

• any number less than 1

Multiple Choice

Does the equation vertically stretch, compress, or reflect?

$$f\left(x\right)=0.75x^2$$   *Compare to the parent function f(x)=x² *

• Stretch by a factor of 2

• Compress by a factor of 0.75

• Reflect across the x-axis

• Both stretch by a factor of 2 and reflect across the x-axis

Multiple Choice

Does the equation vertically stretch, compress, or reflect?

$$f\left(x\right)=\ 2x^2$$   *Compare to the parent function f(x)=x² *

• Stretch by a factor of 2

• Compress by a factor of 2

• Reflect across the y-axis

• Both Stretch by a factor of  $$\frac{1}{2}$$  & Reflect across the x-axis

Multiple Choice

Does the equation vertically stretch, compress, or reflect?

$$f\left(x\right)=-x^2$$  

*Compare to the parent function f(x)=x² *

• Stretch by a factor of 2

• Compress by a factor of  $$-2$$  

• Reflect across the x-axis

• Both Compress by 2 and Reflect across the x-axis

Multiple Choice

Does the equation vertically stretch, compress, or reflect? $$f\left(x\right)=-5x^2$$   *Compare to the parent function f(x)=x² *

• Stretch by a factor of 5

• Compress by a factor of  $$\frac{5}{2}$$  

• Reflect across the x-axis

• Both Stretch by a factor of 5 & Reflect across the x-axis

Multiple Choice

Does the equation vertically stretch, compress, or reflect?

$$f\left(x\right)=\frac{1}{4}x^2$$  

*Compare to the parent function f(x)=x² *

• Stretch by a factor of  $$\frac{1}{4}$$  

• Compress by a factor of  $$\frac{1}{4}$$  

• Reflect across the x-axis

• Both Compress by a factor of 2 & Reflect across the x-axis

Multiple Choice

Does the equation vertically stretch, compress, or reflect? $$f\left(x\right)=0.5x^2$$   *Compare to the parent function f(x)=x² *

• Stretch by a factor of 0.5

• Compress by a factor of 0.5

• Reflect across the x-axis

• Both Compress by a factor of 0.5 & Reflect across the x-axis

Multiple Choice

Does the equation vertically stretch, compress, or reflect?

$$f\left(x\right)=-7x^2$$  

*Compare to the parent function f(x)=x² *

• Stretch by a factor of 7

• Compress by a factor of  $$-7$$  

• Reflect across the x-axis

• Both Stretch by a factor of 7 & Reflect across the x-axis

Multiple Choice

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

• y = x² + 4

• y = (x + 4)²

• y = (x - 4)²

• y = 4x²

Multiple Choice

Given f(x) = (x+2)² - 5.

Describe the transformations from f(x)=x²

• Left 2 and up 5

• Right 2 and down 5

• Left 2 and down 5

• Right 2 and up 5

Multiple Choice

What is the equation of the absolute value function?

• f(x)= |x+4|

• f(x)= |x-4|

• f(x)= |x| + 4

• f(x)= |x| - 4

Multiple Choice

What is the equation of the graph below?

• f(x) = I x + 2 I 

• f(x) = I x + 2 I +2

• f(x) = I x - 2 I +2

• f(x) = I x - 2 I 

Multiple Choice

Describe the transformation from the parent function y = IxI

y = I x + 2 I - 5

• Left 2 up 5

• Right 2 up 5

• Left 2 down 5

• Right 2 down 5

Multiple Choice

What is the equation of the graph below?

• f(x ) = I x + 4 I + 2

• f(x ) = -I x - 4 I + 2

• f(x ) = I x - 4 I + 2

• f(x ) = -I x + 4 I + 2

Multiple Choice

Describe the transformation from the Absolute Value Parent Function.

• Stretches more narrow, shifts up 4 units

• Stretches more narrow, shifts down 4 units

• Compresses wider, shifts up 4 units

• Compresses wider, shifts down 4 units

Multiple Choice

Write an absolute value function given the following transformations:

Reflection across the x-axis, Vertical shift right 2 units, Horizontal shift down 7 units

• y = -|x + 2| - 7 

• y = |x - 2| - 7 

• y = -|x - 2| - 7

• y = -|x - 2| + 7

Multiple Choice

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

• y = x² + 2

• y = -x² + 2

• y = x² - 2

• y = -(x + 2)²

Multiple Choice

If the blue function is f(x)=√x, the red function must be

• g(x)=√(-x)

• g(x)=√(x-1)

• g(x)=√x-1

• g(x)=-√x

Multiple Choice

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

• g(x)=x³+1

• g(x)=x³-1

• g(x)=(x-1)³

• g(x)=(x+1)³

Multiple Choice

Which equation represents this graph.

• f(x)=(x - 4)² - 3

• f(x)=-(x - 4)² + 3

• f(x)=(x - 4)² + 3

• f(x)=-(x + 4)² + 3