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 $$\sqrt{50x^4$y^2$$}$$ 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 $$f(x)$$?

Accepted Answer

Question 15

Solve the inequality $$x^2 + 21$$ \u003e 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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