Q: If $$f(x) = 3x - 7$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

$$f(g(2)) = 3 \times 4 - 7 = 5$$

Q: A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P(t)$$ after $$t$$ hours?

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

Question 1

A roller coaster's height above the ground, $$h(t)$$, in meters, as a function of time $$t in $$seconds, is modeled by $$h(t) = -4.9t^2$ + 24t + 5. $$What is the maximum height the roller coaster reaches?

Accepted Answer

$$h_{max} = 33.4$$

Question 2

Which of the following is the correct equation of a line passing through the point $$(2, 5)$$ with a slope of $$-3$$?

Accepted Answer

$$y = -3x + 11$$

Question 3

Given the function $$f(x) = 2x^2$ - 4x + 1$$, what is the $$x-$$coordinate of the vertex of its graph?

Accepted Answer

$$x = 1$$

Question 4

If $$f(x) = 3x - 7$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 3 	imes 4 - 7 = 5$$

Question 5

Which of the following is the solution set for the inequality $$2x - 5 \u003c 7$$?

Accepted Answer

$$x \u003c 4$$

Question 6

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

Accepted Answer

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

Question 7

Which of the following is the sum of the first 10 terms of the arithmetic sequence where $$a_1 = 5$ and d = 3$?

Accepted Answer

$$S_{10} = 155$$

Question 8

Solve for $$x$$: $$|2x - 3| = 7$$

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 9

Which of the following matrices is the inverse of $$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$?

Accepted Answer

Question 10

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 11

If $$f(x) = x^2$ - 4x + 7$$, what is the axis of symmetry of its graph?

Accepted Answer

$$x = 2$$

Question 12

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount remaining after t$ years. How much remains after 20 years?

Accepted Answer

$$A(20) = 100e$$^{-1}$$ \approx 36.8$$

Question 13

Which of the following is the solution to the system: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (2, 1)$$

Question 14

Which of the following is the sum of the infinite geometric series $$3 + 1.5 + 0.75 + \ldots$$?

Accepted Answer

$$S = 6$$

Question 15

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

Accepted Answer

$$x \geq 1$$

Question 16

A quadratic function models the height (in meters) of a ball thrown upward from a bridge: $$h(t) = -5t^2$ + 20t + 30. $$After how many seconds does the ball hit the ground?

Accepted Answer

$$t = 5$$

Question 17

Which of the following is the correct expansion of $$(x + 2)^3$?

Accepted Answer

$$x^3$$ + $$6x^2 + 12x + 8$

Question 18

If $$\log_2$(x) = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 19

A company finds that the revenue $$R (in $$thousands of dollars) from selling $$x$$ units is $$R(x) = -2x^2$ + 40x. $$What number of units maximizes the revenue?

Accepted Answer

$$x = 20$$

College Algebra: Course Syllabus and Content Overview

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