Quiz about Logarithmic Transformations

Question 1

Describe one of the transformations of the logarithmic function from the parent function.

$$g\left(x\right)=-2\log_3x-1,\ f\left(x\right)=\log_3x$$

Accepted Answer

Reflected over the x-axis

Answer

Translated 1 unit right

Answer

Translated 2 units down

Answer

Horizontal dilation of 1/2

Question 2

Which of the following is NOT a transformation of the log function below?

$$g\left(x\right)=-2\log_3\left(x-1\right)+2,\ f\left(x\right)=\log_3x$$

Accepted Answer

Reflected over the y-axis

Answer

Translated 2 units up

Answer

Vertical dilation by a factor of 2 with respect to the x-axis

Answer

Translated 1 unit right

Question 3

Determine the transformations of the logarithmic functions from their parent function. Check all that apply.

$$g\left(x\right)=\frac{1}{2}\log\ 2\left(x-3\right)-1,\ f\left(x\right)=\ \log\ x$$

Accepted Answer

Vertical dilation by a factor of 1/2

Accepted Answer

Translated 3 units right

Accepted Answer

Translated 1 unit down

Answer

Horizontal dilation by a factor of 2

Question 4

Determine which logarithmic function has the following transformations from this parent function; $$f\left(x\right)=\ \log_2\ x$$

1) Horizontal dilation by a factor of 2 with respect to the y-axis.

2) Reflected over the x-axis.

Accepted Answer

$$g\left(x\right)=-\log_2\ \frac{1}{2}x$$

Answer

$$g\left(x\right)=-\frac{1}{2}\log_{2_{ }}x$$

Answer

$$g\left(x\right)=-\log_22x$$

Answer

$$g\left(x\right)=-2\ \log\ _22x$$

Question 5

Describe the transformations of the logarithmic functions from the parent function. Check all that apply.

$$g\left(x\right)=-\frac{1}{3}\log_5\ -\left(x+2\right)-1$$

Accepted Answer

Reflected over the x-axis

Accepted Answer

Reflected over the y-axis

Accepted Answer

Translated 2 units left and 1 unit down

Answer

Dilated horizontally by a factor of 3

Question 6

Describe the transformations of the logarithmic functions from the parent function. Check all that apply.

$$g\left(x\right)=-\frac{1}{2}\log_5\ -\left(x-1\right)-2$$

Accepted Answer

Reflected over the x-axis.

Accepted Answer

Dilated vertically by a factor of 1/2 with respect to the x-axis.

Accepted Answer

Reflected over the y-axis

Answer

Translated 1 unit left and 2 units down

Logarithmic Transformations