Question 1

Which of the following is the correct interval notation for the solution set of the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$(2, 3)$$

Question 2

A company’s profit $$P (in $$thousands of dollars) is modeled by the function $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

Question 3

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

Accepted Answer

$$x 
eq 3$$

Question 4

Which of the following is the correct solution to the equation $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 5

A quadratic equation $$ax^2 + bx + c = 0$ has discriminant D$$ = $$b^2 - 4ac$. If D$$ \u003c 0$$, what can be said about the solutions?

Accepted Answer

There are two complex (non-real) solutions.

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

$$3x^2 - 2$

Question 8

A line passes through the points $$(2, 5)$$ and $$(6, 13). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 2x + 1$$

Question 9

Which of the following is the correct simplification of $$\sqrt{50} - \sqrt{18}$$?

Accepted Answer

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

Question 10

A rational function $$f(x) = \frac{x^2$ - 4}{x^2$ - 1}$$ has which vertical asymptotes?

Accepted Answer

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

Question 11

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

Accepted Answer

$$x = 2, y = 5$$

Question 12

Which of the following is the correct domain for the function $$f(x) = \sqrt{x - 4}$$?

Accepted Answer

$$x \geq 4$$

Question 13

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

Accepted Answer

$$(x + 1)^2$

Question 14

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

Accepted Answer

$$x = -2$$

Question 15

A rectangular garden has a length that is 3 meters longer than its width. If the area is $$40$$ square meters, what are the dimensions of the garden?

Accepted Answer

Width: $$5 m$$, Length: $$8 m$$

Question 16

Which of the following is the correct simplification of $$\frac{x^2$ - 9}{x^2$ - 6x + 9}$$?

Accepted Answer

$$\frac{(x + 3)(x - 3)}{(x - 3)^2$}$$

Question 17

If $$f(x) = \frac{1}{x}$$ and $$g(x) = x + 2$$, what is $$f(g(3))$$?

Accepted Answer

$$\frac{1}{5}$$

Question 18

Which of the following is the correct solution to the inequality $$2x - 3 \u003e 7$$?

Accepted Answer

$$x \u003e 5$$

Question 19

Which of the following is the correct solution to the equation $$\sqrt{x + 5} = 4$$?

Accepted Answer

$$x = 11$$

College Algebra Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard