Graphing exponential and logarithmic functions

• Vertical Compression

  and Reflection over x-axis

• Vertical Stretch

  and Reflection over x-axis

• Vertical Shift

  and Reflection over x-axis

• No Stretch and Reflection over x-axis.

Describe the transformation(s) for 

 $k\left(x\right)=\log_{10}\left(x-6\right)-4$  .

• k has been shifted 6 units right and 4 units down

• k has been shifted 6 units right and 4 units up

• k has been shifted 6 units left and 4 units down

• k has been shifted 6 units left and 4 units up

Which log function includes the following transformations:
Horizontal stretch by a factor of 3, Horizontal shift right 6 units, Vertical shrink by a factor of 2, vertical shift up 9

•  $f\left(x\right)=\frac{1}{2}\log_2\left(\frac{1}{3}x-2\right)+9$  

•  $f\left(x\right)=\frac{1}{2}\log_2\left(3x-18\right)+9$  

•  $f\left(x\right)=\frac{1}{2}\log_2\left(\frac{1}{3}x-6\right)+9$  

•  $f\left(x\right)=2\log_2\left(3x-6\right)+9$  

Determine the transformation that occurred:

 $\log\left(x\right)\ \rightarrow\ \log\left(x\right)-4$  

• Horizontal shift, 4 units left

• Horizontal shift, 4 units right

• Vertical shift, 4 units up

• Vertical shift, 4 units down

Choose the function that includes all of the transformations from  $f\left(x\right)=\log_4\left(x\right)$  to  $g\left(x\right)$  .
Transformations: Horizontal Shrink by a factor of 3, Reflection over the x-axis, Horizontal shift Left 5 units, Vertical Stretch by a factor of 3 and Vertical shift down 5 units

•  $g\left(x\right)=-3\log_4\left(3x+15\right)-5$  

•  $g\left(x\right)=-3\log_4\left(\frac{1}{3}x+\frac{5}{3}\right)-5$  

•  $g\left(x\right)=3\log_4\left(-3x-15\right)-5$  

•  $g\left(x\right)=3\log_4\left(-\frac{1}{3}x-\frac{5}{3}\right)-5$  

Check ALL of the transformations found in the function below:

 $f\left(x\right)=3\cdot\left(8\right)^{2x}-1$  

• Vertical stretch by 3

• Horizontal compression by 1/2

• Horizontal stretch by 2

• Left 1

• Down 1

• left 2

• down 4

• reflect across y-axis

• reflect across y-axis

• right 2

How did the graph transform from the parent function?

y=2^(x-2)

• Up 2

• Down 2

• Left 2

• Right 2

Using the parent function f(x) = -2(1.5)^x, which function describes a transformation of f(x) moving down 2 units?

• f(x) = -2(1.5)^x + 2

• f(x) = -2(1.5)^x - 2

• f(x) = -2*2(1.5)^x

• f(x) = 1.5(-4)^x

f(x)=log₅(x+4) - 2

Describe the transformation

• translation 4 units to the right, 2 units down

• translation 4 units to the left, 2 units down

• translation 4 units to the up, 2 units right

• translation 4 units to the up, 2 units left