Transformations of Functions Review

Transformations of Functions Review

Open Ended

For the general form below, explain what each letter (a, b, h and k) can do to transform the graph:

y=a f(bx-h)+k

Multiple Select

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

• Horizontal translation left

• Vertical shrink

• Vertical translation down

• Horizontal translation right

• Vertical stretch

Multiple Choice

What is the parent function of the following graph?

• $y=x^2$

• $y=x^3$

• $y=\left|x\right|$

• $y=\frac{1}{x}$

Multiple Choice

What is the correct equation for the transformed graph?

• $y=2\left(x-5\right)^2+4$

• $y=2\left(x+5\right)^2+4$

• $y=-2\left(x-5\right)^2+4$

• $y=-2\left(x+5\right)^2+4$

Multiple Choice

Describe the parent graph transformation

• stretch by 1/2, left 1, down 3
• stretch by 1/2, right 1, down 3
• compression by 1/2, left 1, down 3
• compression by 1/2, right 1, down 3

Multiple Choice

What is the equation of the PARENT  function?

• f(x) = 2^x
• f(x) = x³
• f(x) = |x|
• f(x) = x

Multiple Choice

What are the transformations to the graph compared to the parent function?

• Shifted right 2, shifted up 3, and reflected over the y-axis
• Shifted left 2, shifted up 3, and reflected over the y-axis
• Shifted left 2, shifted up 3, and reflected over the x-axis
• Shifted right 2, shifted up 3, and reflected over the x-axis

Multiple Choice

What function best describes this graph?

• $f\left(x\right)=-\sqrt{x+4}-2$

• $f\left(x\right)=\sqrt{x-4}-2$

• $f\left(x\right)=-\sqrt{x-4}-2$

• $f\left(x\right)=\sqrt{x+4}+2$

Multiple Choice

f(x) = ⅓|x + 9|

• Vertical compression by ⅓ and left 9

• Vertical compression ⅓ and right 9

• Horizontal stretch by 3 and left 9

• Horizontal stretch by 3 and right 9

Multiple Choice

What function has the transformations:

Vertical stretch by 7 and Reflected over x-axis

• $f\left(x\right)\ =\ -7x^2$

• $f\left(x\right)\ =\ 7\left|-x\right|$

• $f\left(x\right)\ =\ \sqrt{-7x}$

• $f\left(x\right)\ =\ -\left|7x\right|$

Multiple Choice

What function has the transformations:

Left 4 and up 7

• $f\left(x\right)\ =\ \left|x+4\right|+7$

• $f\left(x\right)\ =\ \left(x-4\right)^2\ +\ 7$

• $f\left(x\right)\ =\ \left(x+7\right)^2-\ 4$

• $f\left(x\right)\ =\ \left|x+4\right|-7$

Multiple Choice

Describe the transformation of the graph f(x) = -2(x + 5)³

• Vertically compressed by 2, Reflected over y-axis, Right 5

• Vertically stretched by 2, Reflected over x-axis, Left 5

• Vertically stretched by 2, Reflected over x-axis, Right 5

• Vertically compressed by 2, reflected over y-axis, Left 5

Multiple Choice

Which parent function is graphed?

• Linear

• Absolute Value

• Quadratic

• Square Root

Multiple Choice

Identify the transformation from the graph of f(x)=x² to the graph g(x)= -(x+5)²

• shifted up five units

  reflection in x-axis

• shifted down five units

  reflection in x-axis

• shifted left 5 units

  reflection x-axis

• shifted right 5 units

  reflection x-axis

Multiple Choice

Identify the transformations. 

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

Multiple Choice

What type of function is shown?

• cube root
• square root
• logarithm
• exponential

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

If the blue function is f(x)=x², then the red function must be

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²

Multiple Choice

What are the transformations?
y=(x-2)³+4

• Horz shift right 2      Vert shift up 4
• Horz shift left 2    Vert shift up 4
• Horz shift right 2      Vert shift down 4
• Horz shift left 2      Vert shift up 4