Question 1

Given the function $$f(x) = 2^x - 3$$, which of the following best describes its range?

Accepted Answer

$$(-3, \infty)$$

Question 2

Which of the following graphs represents the function $$f(x) = 2^x - 3$$?

Accepted Answer

A graph that passes through $$(0, -2)$$ and has a horizontal asymptote at $$y = -3$$

Question 3

What is the domain of the function $$f(x) = 2^x - 3$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 4

If a scientist models the decay of a substance using $$f(t) = 2$$^{-t}$$, what is the value of f(3$$)$$?

Accepted Answer

$$\dfrac{1}{8}$$

Question 5

Which of the following is the y-intercept of the function $$f(x) = 2^x - 3$$?

Accepted Answer

$$(0, -2)$$

Question 6

A population of bacteria doubles every hour. If the initial population is 50, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 50 \cdot 2^t$$

Question 7

Which of the following statements is true about the function $$f(x) = 2^x - 3$$?

Accepted Answer

The function is always increasing.

Question 8

If $$f(x) = 2^x - 3$$, what is the horizontal asymptote of the graph?

Accepted Answer

$$y = -3$$

Question 9

Suppose the value of a car depreciates according to $$V(t) = 20000 \cdot (0.8)^t$$, where $$t is $$the number of years. What is the value after 3 years?

Accepted Answer

$$10240$$

Question 10

Which of the following best describes the end behavior of $$f(x) = 2^x - 3 as$$ $$x 	o -\infty$$?

Accepted Answer

$$f(x) 	o -3$$

Question 11

If $$f(x) = 2^x - 3$$, for which value of $$x$$ does $$f(x) = 5$$?

Accepted Answer

$$x = 3$$

Question 12

Which of the following is the correct inverse of $$f(x) = 2^x - 3$$?

Accepted Answer

$$f^{-1}(x$$) = \$$log_2(x+3$$)$$

Question 13

A radioactive substance decays according to $$A(t) = 100 \cdot (0.5)^t. $$How much remains after 4 hours?

Accepted Answer

$$6.25$$

Question 14

Which of the following is the solution to $$2^x = 16$$?

Accepted Answer

$$x = 4$$

Question 15

If $$f(x) = 2^x - 3$$, what is $$f(-1)$$?

Accepted Answer

$$-2.5$$

Assessment Review: Exponential and Logarithmic Functions

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