Question 1

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

Accepted Answer

$$x \geq 3$$

Question 2

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

Accepted Answer

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

Question 3

Which of the following is the correct solution set for the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

$$12.2$$ meters

Question 6

Which of the following is the correct graph for the function $$f(x) = -x^2$ + 4x - 3$$?

Accepted Answer

A parabola opening downwards with vertex at $$(2, 1)$$

Question 7

If $$f(x) = 2x^2$ - 5x + 1$$ and $$g(x) = x - 3$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$2(x-3)^2 - 5(x-3) + 1$

Question 8

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

Accepted Answer

$$x = 32$$

Question 9

A car depreciates in value by 15% each year. If its initial value is $$V_0$$, which equation models its value $$V$$ after $$t$$ years?

Accepted Answer

$$V = V_0$ \cdot 0.85^t$$

Question 10

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

Accepted Answer

$$(x, y) = (3, 1)$$

Question 11

Which of the following is the range of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 12

Which of the following is the correct solution for $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2}\ln(7)$$

Question 13

Which of the following is the correct vertex of the quadratic function $$f(x) = x^2$ - 6x + 8$$?

Accepted Answer

$$(3, -1)$$

Question 14

Which of the following is the correct solution to $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 15

Which of the following is the correct solution for the exponential equation $$3^{x+1} = 27$?

Accepted Answer

$$x = 2$$

Question 16

Which of the following is the correct equation for a line passing through $$(2, 5)$$ with a slope of $$-3$$?

Accepted Answer

$$y = -3x + 11$$

Question 17

Which of the following is the correct solution to the inequality $$\frac{x+2}{x-1} \u003e 0$$?

Accepted Answer

$$x  1$$

Question 18

Which of the following is the correct solution for $$\log_{10}(x^2$) = 4$$?

Accepted Answer

$$x = 100 or$$ $$x = -100$$

Question 19

Which of the following is the correct solution for the system $$\begin{cases} x + y = 8 \ x - y = 2 \end{cases}$$?

Accepted Answer

$$(x, y) = (5, 3)$$

College Algebra (MAC 1105) Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard