Question 1

Which of the following best describes the solution set of the quadratic equation $$ax^2 + bx + c = 0$ when b^2$ - 4ac \u003c 0$$?

Accepted Answer

Two complex conjugate solutions

Question 2

A company models its profit $$P (in $$thousands of dollars) as a function of the number of units sold $$x by$$ $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$300 at$$ $$x = 10$$

Question 3

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

Accepted Answer

$$x = 2, y = 1$$

Question 4

If $$f(x) = 2x^2$ - 3x + 5$$ and $$g(x) = x - 4$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 2(-2)^2$ - 3(-2) + 5 = 8 + 6 + 5 = 19$$

Question 5

A cell phone plan charges a base fee of $$\20$ per month plus $$\$$0.10$$ per text message sent. Which function models the total monthly cost $$C$$ for $$x$$ text messages?

Accepted Answer

$$C(x) = 20 + 0.10x$$

Question 6

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

Accepted Answer

$$x 
eq 3$$

Question 7

Given the exponential function modeling radioactive decay $$N(t) = N_0$ e$$^{-kt}$$, which of the following statements is true?

Accepted Answer

The quantity decreases as $$t$$ increases

Question 8

Which of the following is the correct inverse of the function $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-7}{3}$$

Question 9

A ball is thrown upward with an initial velocity of $$32 ft/s $$from a height of $$48 ft. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t + 48. $$When does the ball reach its maximum height?

Accepted Answer

$$t = 1$$ second

Question 10

Which of the following best describes the range of the function $$f(x) = x^2$ - 4x + 7$$?

Accepted Answer

$$y \geq 3$$

Question 11

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

Accepted Answer

$$x = 32$$

Question 12

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x-2)^2$$ + $$(y+3)^2 = 25$

Question 13

A population of bacteria doubles every 3 hours. If the initial population is 500, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{t/3}$$

Question 14

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

Accepted Answer

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

Question 15

If $$f(x) = \sqrt{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 2$$

Question 16

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

Accepted Answer

$$(x-3)(x+3)$$

Question 17

A car depreciates in value by 15% each year. If the car is worth $$\20$$,000$ now, what will its value be after 4 years?

Accepted Answer

$$20,000 	imes (0.85)^4$

Question 18

Which of the following is the solution to the equation $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

Question 19

If $$f(x) = x^2$ and g(x) = x + 1$, what is f(g(3$$))$$?

Accepted Answer

$$16$$

Question 20

Which of the following is the correct solution to the equation $$\frac{3}{x} = 6$$?

Accepted Answer

MAC1105 College Algebra Syllabus and Course Structure Overview

Guida di studio - Domande di pratica

Study guide - Flashcard