Q: Which of the following describes the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - 7$$?

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

Q: A car’s value depreciates by 15% each year. If the car is worth $20,000 now, what will it be worth in 3 years? (Round to the nearest dollar.)

$$20,000 \times (0.85)^3$ \approx 12,281$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 5}$$?

Accepted Answer

$$x \geq 2.5$$

Question 2

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 3$$^{t/4}$$

Question 3

Given the quadratic function $$f(x) = -2x^2$ + 8x - 3$$, what are the coordinates of its vertex?

Accepted Answer

$$(2, 5)$$

Question 4

Which of the following is the inverse of the function $$f(x) = 5x - 7$$?

Accepted Answer

Question 5

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 6

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

Accepted Answer

$$x = 2, y = 1$$

Question 7

Which of the following intervals describes where the function $$f(x) = x^2$ - 4x + 3 is $$decreasing?

Accepted Answer

$$(2, \infty)$$

Question 8

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

Accepted Answer

$$f(g(3)) = 2 \cdot 9 + 1 = 19$$

Question 9

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

Accepted Answer

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

Question 10

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount remaining after t$ years. How much remains after 20 years (rounded to the nearest whole number)?

Accepted Answer

$$A(20) = 100e$$^{-1}$$ \approx 37$$

Question 11

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

Accepted Answer

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

Question 12

Given $$f(x) = \log_2$(x - 1)$$, what is the domain of $$f$$?

Accepted Answer

$$x \u003e 1$$

Question 13

Which of the following describes the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - 7$$?

Accepted Answer

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

Question 14

Solve for $$x$$: $$2^{x+1} = 16$

Accepted Answer

$$x = 3$$

Question 15

Which of the following is the solution to the equation $$\log_3$(x) = 4$$?

Accepted Answer

$$x = 81$$

Question 16

A quadratic equation $$ax^2 + bx + c = 0$ has no real solutions if:

Accepted Answer

$$b^2 - 4ac$$ \u003c 0$$

Question 17

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

Accepted Answer

$$f(2) + g(2) = 4 + 3 = 7$$

Question 18

Which of the following best describes the range of the function $$f(x) = e^x$$?

Accepted Answer

$$(0, \infty)$$

Question 19

A car’s value depreciates by 15% each year. If the car is worth $20,000 now, what will it be worth in 3 years? (Round to the nearest dollar.)

Accepted Answer

$$20,000 	imes (0.85)^3$ \approx 12,281$$

College Algebra Syllabus and Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드