Graphing exponential and logarithmic functions

Select all the transformations that apply.

y = log ₆ (x - 1) - 5

• Horizontal shift left 1

• Horizontal shift right 1

• Vertical shift up 5

• Vertical shift down 5

• Right nine and down seven

• Left nine and down seven

• Left nine and up seven

• Right nine and up seven

• reflect over x axis

• reflect over y axis

• dilate

• translate to the left

 $y=-3\log_{10}\left(x-2\right)+1$  , The transformations of this graph are: the graph expands vertically 3 units, the graph is translated 2 units to the right, and the graph is translated 1 unit up.

• True

• False

How does $f(x)=4(2)^{x-3}-1$ shift the parent function $f\left(x\right)=2^x$ ?  

• Right 3, down 1, stretch by a factor of 4

• Left 3, down 1, stretch by a factor of 4

• Right 3, up 1, stretch by a factor of 4

• Left 3, up 1, stretch by a factor of 4

In the general log function 
y = a*log_b(x-h)+k, what letter tells us if the function has moved left or right?

• a
• b
• h
• k

What type of transformation affects the range of logarithmic function?

• vertical translations

• horizontal translations

• left 3, right 1

• right 3, down 1

• right 3, up 1

• left 3, down 1

This exponential function has a vertical stretch of 4, a decay rate of 1/3, a horizontal shift left 8, and a vertical shift down 1.

• $y=4\left(\frac{1}{3}\right)^{\left(x+1\right)}-8$

• $y=\frac{1}{3}\left(4\right)^{\left(x+8\right)}-1$

• $y=4\left(\frac{1}{3}\right)^{\left(x-8\right)}+1$

• $y=4\left(\frac{1}{3}\right)^{\left(x+8\right)}-1$

Describe the transformation of  $g\left(x\right)=\frac{1}{2}\log\left(x\right)$  when compared to its parent function.

• Vertical stretch by a factor of 1/2

• Vertical compression by a factor of 1/2

• Translate right 1 units

• Translate up 2 units