Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 8}$$?

Accepted Answer

$$x \geq 4$$

Question 2

A company’s revenue $$R (in $$thousands of dollars) is modeled by the function $$R(x) = 50x - x^2$, where x$ 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 $$625$$ thousand dollars at $$x = 25$$ thousand units.

Question 3

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

Accepted Answer

$$(f \circ g)(2) = 11$$

Question 4

Which of the following equations represents a function whose graph is a parabola opening downward?

Accepted Answer

$$y = -3x^2$ + 2x - 1$$

Question 5

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

Accepted Answer

$$x \u003e 1$$

Question 6

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

Accepted Answer

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

Question 7

Solve the equation $$2^{x+1} = 16$ for x$.

Accepted Answer

$$x = 3$$

Question 8

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

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x+7}{5}$$

Question 9

Which of the following best describes the range of the function $$f(x) = \dfrac{1}{x-2}$$?

Accepted Answer

All real numbers except $$0$$

Question 10

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-0.05t}$$, where t$ is in years. If the initial amount is 100$ grams, how much remains after 20$ years (rounded to the nearest gram)?

Accepted Answer

$$37$$ grams

Question 11

Which of the following is NOT a function?

Accepted Answer

A relation where $$x = 2$$ maps to both $$y = 3$$ and $$y = 5$$

Question 12

Solve the inequality $$3x - 5 \u003c 7.$$

Accepted Answer

$$x \u003c 4$$

Question 13

Which transformation occurs when the graph of $$f(x) = x^2$ is changed to g(x$$) = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 14

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

Accepted Answer

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

Question 15

Which of the following is the solution set for $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 16

A car’s value depreciates exponentially according to $$V(t) = 20000 \cdot (0.85)^t$$, where $$t is $$the number of years after purchase. What is the value of the car after 3 years (rounded to the nearest dollar)?

Accepted Answer

$$12250$$

Question 17

Which of the following is the solution to the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 3, y = 2$$

Question 18

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

Accepted Answer

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

Question 19

If $$f(x) = \dfrac{2x}{x+1}$$, what is the value of $$f^{-1}(2$$)$$?

Accepted Answer

$$f^{-1}(2) = 2$

Question 20

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

Accepted Answer

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

College Algebra Syllabus and Course Structure – Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard