Question 1

Given the endpoints of a line segment at $$A(2, -3)$$ and $$B(-4, 5)$$, what is the length of the segment $$AB$$?

Accepted Answer

$$\sqrt{(2 + 4)^2$ + (-3 - 5)^2$} = \sqrt{36 + 64} = \sqrt{100} = 10$$

Question 2

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x-3}$$?

Accepted Answer

$$\{x \mid x 
eq 3\}$$

Question 3

Find the equation of the line that passes through the points $$(1, 2)$$ and $$(4, 8).$$

Accepted Answer

$$y = 2x$$

Question 4

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - 7 as$$ $$x 	o -\infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 5

Solve the quadratic equation $$x^2 - 6x + 5 = 0$.

Accepted Answer

$$x = 1 or$$ $$x = 5$$

Question 6

Given $$f(x) = x^2$ and g(x) = x + 1$, find (f$$ \circ g)(2)$$.

Accepted Answer

$$(f \circ g)(2) = f(g(2)) = f(3) = 9$$

Question 7

Which of the following is the inverse of the function $$f(x) = 2x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x - 7}{2}$$

Question 8

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-0.03t}$$. What is the half-life of the substance (rounded to the nearest year)?

Accepted Answer

$$t = \dfrac{\ln 2}{0.03} \approx 23$$

Question 9

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 1$$

Question 10

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

Accepted Answer

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

Question 11

Given the sequence defined recursively by $$a_1 = 2$, a$$_{n+1} = 3a_n + 1$$, what is a_3$?

Accepted Answer

$$a_3 = 22$

Question 12

Which of the following is the correct logarithmic form of the exponential equation $$5^x = 20$$?

Accepted Answer

$$x = \log_5$ 20$$

Question 13

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -2x^2$ + 12x + 20$$, where $$x is $$the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $$R(3) = 38 at$$ $$x = 3$$ thousand units

Question 14

Which of the following is the result of dividing $$2x^3$$ - $$3x^2 + 4x - 5$ by x - 2$ using synthetic division?

Accepted Answer

$$2x^2 + x + 6$$ + \dfrac{7}{x-2}$$

Question 15

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 16

Solve the rational equation $$\dfrac{x}{x-2} = 3.$$

Accepted Answer

$$x = 3$$

Question 17

Which of the following is the solution set for the inequality $$\dfrac{x+1}{x-2} \u003e 0$$?

Accepted Answer

$$x  2$$

Question 18

Given the system $$\begin{cases} x^2$ + y^2$ = 25 \ x - y = 1 \end{cases}$$, which of the following is a solution?

Accepted Answer

$$(x, y) = (\dfrac{1 + \sqrt{101}}{2}, \dfrac{-1 + \sqrt{101}}{2})$$

Question 19

Simplify the expression $$\sqrt{50} + 2\sqrt{8}.$$

Accepted Answer

$$7\sqrt{2}$$

UNLV Math 124: College Algebra Syllabus and Core Topics Study Guide

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