Question 1

Which of the following is the correct definition of a function?

Accepted Answer

A relation in which each input is paired with exactly one output.

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 17$$

Question 3

A company models its profit $$P (in $$thousands of dollars) as a function of the number of units sold $$x by$$ $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

Question 4

Which of the following describes the transformation of the graph of $$y = x^2$ to y$$ = $$-2(x-3)^2 + 4$?

Accepted Answer

Reflect over the $$x-$$axis, stretch vertically by a factor of $$2$$, shift right $$3$$ units, and up $$4$$ units.

Question 5

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

Accepted Answer

$$(f \circ g)(2) = 11$$

Question 6

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x-4}$$?

Accepted Answer

$$x 
eq 4$$

Question 7

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 3$$^{t/4}$$

Question 8

Which of the following is the inverse of the function $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x-5}{2}$$

Question 9

A car depreciates in value according to the function $$V(t) = 25000 \cdot (0.85)^t$$, where $$t is $$the number of years after purchase. What is the value of the car after 3 years?

Accepted Answer

$$V(3) = 25000 \cdot (0.85)^3$ \approx 15316$$

Question 10

Which of the following equations represents a line passing through the points $$(2, 5)$$ and $$(6, 13)$$?

Accepted Answer

$$y = 2x + 1$$

Question 11

Solve the quadratic equation $$x^2 - 6x + 8 = 0$.

Accepted Answer

$$x = 2 or$$ $$x = 4$$

Question 12

Which of the following is the correct graph for the function $$y = |x-3|$$?

Accepted Answer

A V-shaped graph with vertex at $$(3, 0)$$ opening upwards.

Question 13

If $$f(x) = \sqrt{x-1}$$, what is the implied domain of $$f$$?

Accepted Answer

$$x \geq 1$$

Question 14

A chemical reaction is modeled by $$C(t) = 100e$$^{-0.05t}$$, where C$ is the concentration in mg/L and t$ is time in minutes. What is the concentration after 20 minutes?

Accepted Answer

$$C(20) = 100e$$^{-1}$$ \approx 36.79 mg/L$$

Question 15

Which of the following is the solution to the equation $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 16

Given the rational function $$f(x) = \dfrac{x^2$ - 9}{x^2$ - 4}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 17

A savings account earns interest compounded annually at a rate of $$6\%. If $$you deposit $$\1000$, how much will you have after 5$ years? (Use A = P(1 + r)^t$)

Accepted Answer

$$A = 1000(1.06)^5$ \approx 1338.23$$

Question 18

Which of the following is the correct composition $$(g \circ f)(x) if$$ $$f(x) = x + 2$$ and $$g(x) = x^2$?

Accepted Answer

$$(g \circ f)(x) = (x + 2)^2$

Question 19

Which of the following statements is true about the graph of $$y = \log(x)$$?

Accepted Answer

It has a vertical asymptote at $$x = 0$$ and passes through $$(1, 0).$$

College Algebra Syllabus and Course Structure Study Guide

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