Reteach 10.3

If g(x) is a transformation of f(x), describe the transformation.

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

• Up 4 units

• Down 4 units

• Left 4 units

• Right 4 units

The graph

 $g\left(x\right)=2^{\left(x-3\right)}$ is shown, which statement best describes the transformation from the parent graph  $f\left(x\right)=2^x$ .

• Vertically shift up 3

• Vertically shift down 3

• Horizontally shift right 3

• Horizontally shift left 3

Which graph best represents

 $y=2^x-4$  

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Which of the following is NOT a transformation of the equation

 $f\left(x\right)=3\cdot2^{\left(x-3\right)}+3$  

• Shift horizontally left 3 units

• Shift vertically up 3 units

• Shift horizontally right 3 units

• Vertically stretched by a factor of 3

Which of the following describes the transformation of  $f\left(x\right)=\frac{1}{2}\cdot2^{\left(x+2\right)}-3$  from the parent graph  $g\left(x\right)=2^x$  

• Vertically shift down 3, horizontally shift left 2, and vertically compressed 1/2 units

• Vertically shift up 3, horizontally shift left 2, and vertically compressed 1/2 units

• Vertically shift down 3, horizontally shift right 2, and vertically compressed 1/2 units

• Vertically shift up 3, horizontally shift right2, and vertically compressed 1/2 units

Which equation matches the transformations:

Reflected across the x-axis, vertical stretch by 3, right 2, up 1.

• $y=-3\cdot4^{\left(x+2\right)}+1$

• $y=-3\cdot4^{\left(x-2\right)}+1$

• $y=-3^{\left(x-2\right)}+1$

• $y=3\cdot4^{\left(-\left(x+2\right)\right)}+1$

The square root parent function f(x) was transformed to become g(x). Which equation matches the transformation?

• $y=\sqrt{x+3}+2$

• $y=\sqrt{x-3}-2$

• $y=\sqrt{x-3}-2$

• $y=\sqrt{x+3}-2$

The square root parent function is

 $f\left(x\right)=\sqrt{x}$  , what would the function be if it was vertically stretched by 3, translated left 4 and up 2?

•  $y=\sqrt{3\left(x+4\right)}+2$  

•  $y=\sqrt{\frac{1}{3}\left(x+4\right)}+2$  

•  $y=3\sqrt{x-4}+2$  

•  $y=3\sqrt{x+4}+2$  

Check all the transformations that apply to the following:

 $f\left(x\right)=-\frac{1}{3}\left(2\right)^{\left(x+6\right)}-5$  

• reflection across x-axis

•  $vertical\ compress\ by\ \frac{1}{2}$  

•  $horizontal\ compress\ by\ \frac{1}{2}$  

• vertical stretch by 2

• reflection across y-axis

Check all of the transformations that are true for the following:

 $y=-\frac{1}{5}\left(3\right)^{\left(x-7\right)}+10$  

• translated left 7 units

• translated right 7 units

• reflection across x-axis

• reflection across y-axis

• vertical compression of 1/5