Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following is the correct definition of a polynomial function?

Accepted Answer

A function that can be written as $$f(x) = a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$$, where $$a_i$$ are real numbers and $$n$ is a non-negative integer.

Question 2

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

Accepted Answer

$$x \geq 3$$

Question 3

A company models its profit $$P (in $$thousands of dollars) as $$P(x) = -2x^2$ + 8x + 10$$, 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

Maximum profit is $$18$$ thousand dollars at $$x = 2$$ thousand units.

Question 4

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 5

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

A population of bacteria triples every 4 hours. If the initial population is 200, what will the population be after 12 hours?

Accepted Answer

$$5400$$

Question 8

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

Accepted Answer

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

Question 9

If $$f(x) = x^2$ - 4x + 3$$ and $$g(x) = 2x - 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$4x^2 - 20x + 24$

Question 10

Which of the following is the solution to the equation $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 11

A quadratic equation $$ax^2 + bx + c = 0$ has real and equal roots. Which of the following must be true?

Accepted Answer

$$b^2 - 4ac = 0$

Question 12

A car depreciates in value by 15% each year. If the car is currently worth $$\20$$,000$, what will its value be after 3 years?

Accepted Answer

$$\12$$,282.50$

Question 13

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

Accepted Answer

$$x = 3$$

Question 14

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

Accepted Answer

$$x = 3$$

Question 15

A student invests $$\1000$ in an account that pays 6% annual interest compounded quarterly. What will the balance be after 2 years? (Round to the nearest dollar)

Accepted Answer

$$\1127$

Question 16

Which of the following is the solution set for the equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2,\ x = 3$$

Question 17

Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 18

A patient is given a dose of medication that decays exponentially in the body according to $$A(t) = 50e$$^{-0.2t}$$, where A$ is the amount in mg and t$ is time in hours. How much medication remains after 5 hours? (Round to the nearest mg)

Accepted Answer

$$18 mg$$

Question 19

Which of the following is the solution to the equation $$\sqrt{x+1} = 5$$?

Accepted Answer

$$x = 24$$

College Algebra Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard