Question 1

Which of the following is the correct definition of the domain of a function $$f(x)$$?

Accepted Answer

The set of all $$x$$ values for which $$f(x) is $$defined.

Question 2

A hospital records the number of patients admitted each day as a function $$P(d)$$, where $$d is $$the day of the month. If $$P(15) = 42$$, what does this value represent?

Accepted Answer

42 patients were admitted on the 15th day of the month.

Question 3

Which of the following equations represents a linear function?

Accepted Answer

$$f(x) = 2x + 5$$

Question 4

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

Accepted Answer

$$C = 30 + 0.20m$$

Question 5

Given the quadratic function $$f(x) = x^2$ - 6x + 8$$, what are its zeros?

Accepted Answer

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

Question 6

A biologist models the population of a species with the exponential function $$P(t) = 500e$$^{0.03t}$$, where t$ is time in years. What is the population after 10 years?

Accepted Answer

$$P(10) = 500e$$^{0.3}$$ \approx 674$$

Question 7

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

$$x = 3, y = 1$$

Question 8

A medication’s concentration in the bloodstream decreases exponentially according to $$C(t) = 100e$$^{-0.5t}$$, where t$ is in hours. What is the concentration after 4 hours?

Accepted Answer

$$C(4) = 100e$$^{-2}$$ \approx 13.53$$

Question 9

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

Accepted Answer

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

Question 10

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 for how many units sold does it occur?

Accepted Answer

Maximum profit is $$P(3) = 2$$ thousand dollars, at $$x = 3$$ thousand units.

Question 11

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

Accepted Answer

$$x = 6$$ and $$x = -1$$

Question 12

A scientist mixes two solutions: one with 30% salt and one with 10% salt. How many liters of each should be mixed to obtain 20 liters of a 15% salt solution?

Accepted Answer

5 liters of 30% solution and 15 liters of 10% solution

Question 13

Which of the following is the correct inverse of the function $$f(x) = 3x - 4$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 4}{3}$$

Question 14

A parabola opens upward and has vertex at $$(2, -3). $$Which equation could represent this parabola?

Accepted Answer

$$y = (x - 2)^2$ - 3$$

Question 15

Which of the following is the correct solution to the inequality $$3x - 7 \u003c 2x + 5$$?

Accepted Answer

$$x \u003c 12$$

Question 16

A radioactive substance decays according to $$A(t) = 200e$$^{-0.1t}$$, where t$ is in years. How long will it take for the substance to decay to half its original amount?

Accepted Answer

$$t = \frac{\ln(0.5)}{-0.1} \approx 6.93$$ years

Question 17

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

Accepted Answer

$$x = 32$$

Question 18

A rectangle has a length that is 3 units more than twice its width. If the perimeter is 36 units, what are the rectangle’s dimensions?

Accepted Answer

Width = 5 units, Length = 13 units

Question 19

Which of the following is the correct solution to the equation $$x^2 + 4x + 5 = 0$?

Accepted Answer

$$x = -2 \pm i$$

Math 0031: College Algebra - Schedule and Practice Problems Overview

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