Quiz about 2025 Key Features of Exponential Functions

Question 1

Given the function

$$f\left(x\right)=\ 2\ \left(2\right)^x$$

Which of the following statements are true about the function's graph?

Accepted Answer

The graph has a y-intercept at (0,2)

Accepted Answer

The graph has a horizontal asymptote at

y = 0

Answer

The graph is decreasing for all real numbers

Answer

The graph has a decay rate of 200%

Answer

The graph is negative for all real numbers

Question 2

Given the function

$$f\left(x\right)\ =\ 2\ \left(\frac{1}{3}\right)^x$$

Which of the following statements are true about the functions graph?

Accepted Answer

The graph has a decay factor of 66.6%

Accepted Answer

The graph is decreasing for all real numbers.

Accepted Answer

As $$x\rightarrow+\infty\ ,\ y\rightarrow0$$

Answer

The graph is negative for all real numbers

Answer

The graph has a y-intercept at (0,1)

Question 3

Using the graph, which statements are true?

Accepted Answer

$$f\left(x\right)\ =\ 4\ \cdot\ \left(\frac{1}{2}\right)^x$$

represents the graph

Accepted Answer

The graph has an horizontal asymptote at y = 0

Answer

The graph is increasing on all real numbers

Answer

The domain is $$x\ >\ 2$$

Answer

The graph is negative for all real numbers

Question 4

Given the function

$$f\left(x\right)\ =\ 2\cdot2^x+2$$

Which of the following statements is true?

Accepted Answer

The graph has a horizontal asymptote at y = 2

Answer

The graph has a y-intercept at (0,2)

Answer

The graph has an x-intercept at (2,0)

Answer

The graph is increasing because it has a factor less than between 0 and 1.

2025 Key Features of Exponential Functions