Question 1

Which of the following sets represents the domain of the function $f(x) = \sqrt{x-2}$?

Accepted Answer

$x \geq 2$

Question 2

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

Accepted Answer

$19$

Question 3

Which of the following is the correct factorization of $x^2 + 10x + 25$?

Accepted Answer

$(x + 5)^2$

Question 4

Simplify the expression $\dfrac{2x^2 - 8}{x^2 - 4}$.

Accepted Answer

$2$

Question 5

A toy rocket is launched from a platform 8 ft above the ground with an initial velocity of 48 ft/sec. Its height after $t$ seconds is given by $h(t) = -16t^2 + 48t + 8$. What is the maximum height reached by the rocket?

Accepted Answer

$44$ ft

Question 6

Which of the following intervals describes where the function $f(x)$ is decreasing, given the graph below shows $f(x)$ decreasing from $x = -2$ to $x = 1$?

Accepted Answer

$(-2, 1)$

Question 7

Solve for $x$: $\sqrt{x - 2} = 3$.

Accepted Answer

$x = 7$

Question 8

Which of the following is the correct simplification of $\sqrt{50x^4y^2}$ for positive $x$ and $y$?

Accepted Answer

$5x^2y\sqrt{2}$

Question 9

If $f(x) = x^2 - 2x - 3$, what are the $x$-intercepts of the parabola?

Accepted Answer

$x = -1$ and $x = 3$

Question 10

Which of the following is the correct result of multiplying $(2x + 3y)(2x - 3y)$?

Accepted Answer

$4x^2 - 9y^2$

Question 11

Rationalize the denominator: $\dfrac{8}{\sqrt{27}}$.

Accepted Answer

$\dfrac{8\sqrt{3}}{9}$

Question 12

Express $\sqrt[3]{x^5}$ in terms of rational exponents.

Accepted Answer

$x^{5/3}$

Question 13

Which of the following is the correct solution to the equation $2x + 1 = 9$?

Accepted Answer

$x = 4$

Question 14

Given $f(x) = x^3 + 5x + 1$, which of the following is a zero of $f(x)$?

Question 15

Solve the inequality $x^2 + 21 > 10x$ and express the solution in interval notation.

Accepted Answer

$(-\infty, 3) \cup (7, \infty)$

Question 16

Which of the following is the correct simplification of $\dfrac{x^2 - 1}{x^2 + x - 2}$?

Accepted Answer

$\dfrac{x+1}{x+2}$

Question 17

A 16-foot tree casts a shadow that is 12 feet long. What is the distance from the top of the tree to the end of the shadow?

Accepted Answer

$\sqrt{16^2 + 12^2}$ ft

Question 18

Which of the following equations has a vertical asymptote at $x = 0$ and a horizontal asymptote at $y = 0$?

Accepted Answer

$f(x) = \dfrac{1}{x}$

Question 19

Which of the following is the correct simplification of $\sqrt{45} - \sqrt{20}$?

Accepted Answer

$3\sqrt{5} - 2\sqrt{5} = \sqrt{5}$

College Algebra Final Exam Review: Functions, Equations, Polynomials, and Applications

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