Question 1

Which of the following is the correct solution to the quadratic equation $$2x^2 - 4x - 6 = 0$?

Accepted Answer

$$x = -1,\ x = 3$$

Question 2

A business models its profit $$P (in $$thousands of dollars) as a function of the number of units sold $$x by$$ $$P(x) = -2x^2$ + 12x - 8. $$What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$10$$ thousand dollars at $$x = 3$$ units

Question 3

Which of the following is the correct domain for the function $$f(x) = \sqrt{5 - x}$$?

Accepted Answer

$$(-\infty, 5]$$

Question 4

Given the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$, what is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1)$$

Question 5

Which of the following is the correct equation of a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 6

A population of bacteria doubles every 3 hours. If the initial population is 500, which exponential function models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{t/3}$$

Question 7

Which of the following is the correct inverse of the function $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 8

If $$f(x) = x^2$ and g(x) = x + 1$, what is the composite function (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (x + 1)^2$

Question 9

Which of the following is the correct solution to the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 10

A chemical reaction decays at a rate modeled by $$A(t) = 100e$$^{-0.2t}$$, where A$ is the amount remaining after t$ hours. How much remains after 5$ hours (rounded to the nearest whole number)?

Accepted Answer

$$37$$

Question 11

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 12

Given the function $$f(x) = \frac{2x + 1}{x - 3}$$, what is the vertical asymptote?

Accepted Answer

$$x = 3$$

Question 13

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

Accepted Answer

$$x = 32$$

Question 14

A line passes through the points $$(1, 2)$$ and $$(3, 8). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 3x - 1$$

Question 15

Which of the following is the correct solution to the equation $$x^2 + 4 = 0$?

Accepted Answer

$$x = 2i,\ x = -2i$$

Question 16

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

Accepted Answer

$$10$$

Question 17

Which of the following is the correct solution to the rational equation $$\frac{x}{x - 2} = 3$$?

Accepted Answer

Question 18

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-kt}$$. If the half-life is 10$ years, what is the value of k$?

Accepted Answer

$$k = \frac{\ln 2}{10}$$

Question 19

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

Accepted Answer

Shift right $$3$$ units and up $$2$$ units

College Algebra & Precalculus Syllabus and Course Structure Study Guide

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