Graphing exponential and logarithmic functions

You are transforming a logarithmic function to be shifted LEFT 4 and DOWN 2. Which function could you graph?

For f(x)=a(b)^x + k how does adding a constant (k) transform the parent function?

• vertical shift

• horizontal shift

• reflect over x axis

Match the following log functions to their translation types,

• Shift Left

• Shift Right

• Moves Down

Describe the transformations from the parent function y=log₆x to y = - log ₆ (x - 1) - 5

• Reflection about the x-axis; shift left one and up five

• Reflection about the x-axis; shift left one and down five

• Reflection about the y-axis; shift right one and down five

• Reflection about the x-axis; shift right one and down five

 $f\left(x\right)\ =\ \log\ x$  

 $g\left(x\right)\ =\ -f\left(x\right)\ +\ 8$  Describe how f(x) is transformed to g(x).

• f(x)  is reflected across x-axis and moved down 8 units to create g(x)

• f(x)  is reflected across y-axis and moved down 8 units to create g(x)

• f(x)  is reflected across x-axis and moved up 8 units to create g(x)

• f(x)  is reflected across y-axis and moved up 8 units to create g(x)

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

f(x)=2ln(x+2)

Describe the transformation

• Vertical Stretch by 2, translation 2 units to the left

• Vertical Compression by 2, translation 2 units to the left

• Vertical Stretch by 2, translation 2 units to the right

• Vertical Compression by 2, translation 2 units to the right

Reflecting over the y-axis changes the ____-_____________. 

• x-axis
• x-coordinate
• y-coordinate
• none of the above

 $y=3^x$  is transformed to $y=\left(-2\right)3^{x-14}+10$  describe the transformation of the graph.

• Vertical Reflection, Vertical Stretch, Right 14 units, Up 10 units.

• Horizontal Reflection, Vertical Stretch, Right 14 units, Up 10 units.

• Vertical Reflection, Vertical Stretch, Left 14 units, Down 10 units.