Quiz about Graphing Exponential and Logarithmic Functions with Transformations

Question 1

Which graph best represents the following logarithmic function?
$$y=\log_4x$$

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 2

Which graph best represents the following logarithmic function?
$$y=\log_2x$$

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 3

Determine the transformation that occurred:

Accepted Answer

Vertical shift, 4 units down

Answer

Horizontal shift, 4 units left

Answer

Horizontal shift, 4 units right

Answer

Vertical shift, 4 units up

Question 4

How did the graph transform from the parent function?

y=2^(x-2)

Accepted Answer

Right 2

Answer

Up 2

Answer

Down 2

Answer

Left 2

Question 5

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

Accepted Answer

f(x) = -2(1.5)^x - 2

Answer

f(x) = -2(1.5)^x + 2

Answer

f(x) = -2*2(1.5)^x

Answer

f(x) = 1.5(-4)^x

Question 6

Which function represents a horizontal dilation of the function above?

Accepted Answer

C) f(x) = f(x/2)

Answer

A) f(x) = 2f(x/2)

Answer

B) f(x) = f(2x)

Answer

D) f(x) = f(x + 2)

Question 7

Write the equation of the transformation of the parent function y = loge x that is reflected across the x-axis, shifted 3 units up, and then shifted 1 unit right.

Accepted Answer

- ln (x - 1) + 3

Answer

- ln (x - 1) - 3

Answer

- ln (x + 1) + 3

Answer

ln (-x - 1) + 3

Question 8

Compared to its parent function what transformation would be caused by this functions a-value?

Accepted Answer

Vertical Compression

and Reflection over x-axis

Answer

Vertical Stretch

and Reflection over x-axis

Answer

Vertical Shift

and Reflection over x-axis

Answer

No Stretch and Reflection over x-axis.

Question 9

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 10

Check ALL of the transformations found in the function below:
f\left(x\right)=3\cdot\left(8\right)^{2x}-1

Accepted Answer

Vertical stretch by 3

Accepted Answer

Horizontal compression by 1/2

Accepted Answer

Down 1

Answer

Horizontal stretch by 2

Answer

Left 1

Question 11

For $$y=a\left(b\right)^x+k$$ , how does adding a constant "k" transform the parent function?

Accepted Answer

Vertical Translation

Answer

Horizontal shift

Answer

Vertical Dilation

Answer

Horizontal Dilation

Question 12

Looking at the graph, what is the asymptote?

Accepted Answer

x = 1

Answer

y = 1

Answer

x = -1

Answer

y = -1

Question 13

Match the graph with its equation

Accepted Answer

y = log₄ (x + 2) + 1

Answer

y = log₄ (x)+2

Answer

y = log₄ (x - 1) + 2

Answer

y = log₄ (-x + 2)

Graphing Exponential and Logarithmic Functions with Transformations

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