Question 1

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

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the quadratic function $$f(x) = 2x^2$ - 4x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1, -1)$$

Question 3

Which of the following best describes the graph of an exponential function $$f(x) = a \, b^x$$ where $$a \u003e 0$$ and $$b \u003e 1$$?

Accepted Answer

It is a curve that increases rapidly as $$x$$ increases.

Question 4

A biologist models the population of bacteria in a petri dish using $$P(t) = 500 \, e$$^{0.3t}$$, where t$ is in hours. What is the population after 5 hours?

Accepted Answer

$$500 \, e$$^{1.5}$$ \approx 2240$$

Question 5

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

Accepted Answer

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

Question 6

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit and at how many units sold does it occur?

Accepted Answer

Maximum profit is $$8 at$$ $$x = 3$$

Question 7

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

Accepted Answer

$$x = 4$$

Question 8

A medical researcher finds that the concentration of a drug in the bloodstream decreases exponentially according to $$C(t) = 100 \, e$$^{-0.2t}$$, where t$ is in hours. What is the half-life of the drug?

Accepted Answer

$$t = \frac{\ln 2}{0.2} \approx 3.47$$ hours

Question 9

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 10

A quadratic equation models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$h = 21.9$$ meters

Question 11

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 12

Which of the following is the correct logarithmic form of the exponential equation $$5^x = 20$$?

Accepted Answer

$$x = \log_{5} 20$$

Question 13

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

Accepted Answer

$$V = 20000 \, (0.85)^3$ \approx 15313$$

Question 14

Which of the following is the correct composition of the functions $$f(x) = x^2$ and g(x) = x + 1$ evaluated at x = 2$ for f(g(x$$))$$?

Accepted Answer

$$f(g(2)) = (2 + 1)^2$ = 9$$

Question 15

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 16

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

Accepted Answer

$$f(x) \geq 0$$

Question 17

A scientist fits a linear model to data relating temperature $$T (in$$ °C) and reaction rate $$R (in $$mol/s): $$R = 0.5T + 2. $$What is the reaction rate when $$T = 10$$?

Accepted Answer

$$R = 0.5 	imes 10 + 2 = 7$$

Question 18

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

Accepted Answer

$$(x - 3)(x + 3)$$

Question 19

Which of the following is the correct solution to $$\log_{3} x = 4$$?

Accepted Answer

$$x = 81$$

College Algebra (MAC 1105) Syllabus and Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드