Question 1

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

Accepted Answer

A relation in which each input is paired with exactly one output.

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 17$$

Question 3

Which of the following equations represents a line with a slope of $$-3$$ and a $$y-$$intercept of $$4$$?

Accepted Answer

$$y = -3x + 4$$

Question 4

A chemical reaction's temperature $$T (in $$degrees Celsius) is modeled by $$T(t) = 5t^2$ + 2t + 20$$, where $$t is $$time in hours. What is the temperature after 3 hours?

Accepted Answer

$$T(3) = 59$$

Question 5

Which of the following is the solution set for the inequality $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

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 for $$x$$: $$\frac{2x - 1}{3} = 5$$

Accepted Answer

$$x = 8$$

Question 8

Which of the following is the vertex of the parabola $$y = (x - 2)^2$ + 5$$?

Accepted Answer

$$(2, 5)$$

Question 9

A medication's concentration in the bloodstream is modeled by $$C(t) = 50e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 5 hours? (Round to the nearest whole number.)

Accepted Answer

$$C(5) \approx 18$$

Question 10

Which of the following is the solution to the quadratic equation $$x^2 - 6x + 8 = 0$?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 11

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 30 + 0.20m$$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

$$(f \circ g)(2) = 9$$

Question 14

Which of the following best describes the graph of $$y = |x - 3|$$?

Accepted Answer

A V-shaped graph with vertex at $$(3, 0)$$

Question 15

A student invests $$\1000$ in an account that earns 6$$\%$$ annual interest compounded yearly. Which formula gives the amount A$ after t$ years?

Accepted Answer

$$A = 1000(1.06)^t$$

Question 16

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

Accepted Answer

$$x = 3, y = 1$$

Question 17

Which of the following is the domain of the function $$f(x) = \frac{1}{x - 4}$$?

Accepted Answer

All real numbers except $$x = 4$$

Question 18

A rectangle has a length that is 3 times its width. If the perimeter is 64 units, what is the area?

Accepted Answer

192 square units

Question 19

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

Accepted Answer

$$x = 32$$

Question 20

A ball is thrown upward from a height of 2 meters with an initial velocity of 10 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 10t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

7.1 meters

College Algebra Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard