Transformations of Functions

If the original function is f(x) then state the transformation that takes f(x) to g(x) = |-x + 3|

• Reflect over y-axis
  Left 3
• Reflect over y-axis
  Right 3
• Reflect over x-axis
  Left 3
• Reflect over x-axis
  Right 3

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

Which transformation will occur if f(x) = x² is replaced with 2⋅f(x)?

• Vertical Compression by a factor of 2

• Vertical Stretch by a factor of 2

• Vertical translation up by 2 units

• Reflection across the x-axis

Which transformation will occur if f(x) = x² is replaced with 1/2⋅f(x)?

• Vertical Compression by a factor of 1/2

• Vertical Stretch by a factor of 1/2

• Vertical translation up by 2 units

• Reflection across the x-axis

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

• x³ + 3
• x³ - 3
• (x + 3)³
• (x - 3)³

Tags

CCSS.HSF.BF.B.3

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

• x³+7
• x³-7
• (x-7)³
• (x+7)³

Tags

CCSS.HSF.BF.B.3

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

y = -2 I x - 3 I + 3

• 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, compression by 1/2, right 3, up 3

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

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

• $y=-\left|x-15\right|-3$

• $y=-\left|x+15\right|-3$

• $y=\frac{1}{2}\left|x+3\right|-15$

• $y=\frac{1}{2}\left|x-3\right|-15$

• $y=\left|-x-15\right|-3$

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

• Horizontal translation left

• Vertical compression

• Vertical translation down

• Horizontal translation right

• Vertical stretch

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

• translates left 1 unit and down 9 units

• translates right 1 unit and down 9 units

• translates up 1 unit and right 9 units

• translates down 1 unit and left 9 units

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

• Compresses the graph vertically by a factor of 1/3 and translates up 4 units

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

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

• Translates the graph right 3 units and down 4 units