Question 1

Which of the following statements best describes the difference between a relation and a function?

Accepted Answer

A relation is any set of ordered pairs, while a function is 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 the domain of $$f$$?

Accepted Answer

All real numbers $$x$$ such that $$x \in \mathbb{R}$$

Question 3

A hospital uses the function $$C(t) = 500e$$^{0.04t}$$ to model the cost of a certain treatment after t$ years. What is the cost after 5 years, rounded to the nearest dollar?

Accepted Answer

$$C(5) = 500e$$^{0.2}$$ \approx 610$$

Question 4

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$ + 4$$

Question 5

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

Accepted Answer

$$(f \circ g)(x) = 3x^2$ - 2$$

Question 6

A company’s revenue is modeled by $$R(x) = 100x - 0.5x^2$, where x$ is the number of units sold. What is the maximum revenue, and for how many units is it achieved?

Accepted Answer

Maximum revenue is $$R(100) = 5000 at$$ $$x = 100$$ units.

Question 7

Which of the following is the inverse of the function $$f(x) = 2x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{2}$$

Question 8

A biologist models the population of bacteria with $$P(t) = 2000 \cdot 3^t. If $$the population doubles every hour, what is the population after 2 hours?

Accepted Answer

$$P(2) = 2000 \cdot 3^2$ = 2000 \cdot 9 = 18000$$

Question 9

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 10

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

Accepted Answer

Shift right by 3 units and up by 2 units.

Question 11

A pharmaceutical company uses the function $$Q(t) = 1000e$$^{-0.05t}$$ to model the quantity of a drug remaining in the body after t$ hours. What is the quantity after 10 hours, rounded to the nearest whole number?

Accepted Answer

$$Q(10) = 1000e$$^{-0.5}$$ \approx 607$$

Question 12

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

Accepted Answer

$$x \u003c 7$$

Question 13

If $$f(x) = \sqrt{x - 4}$$, what is the domain of $$f$$?

Accepted Answer

All real numbers $$x$$ such that $$x \geq 4$$

Question 14

A chemical reaction is modeled by $$C(t) = 50 \ln(t + 1)$$, where $$t is $$time in minutes. What is the concentration after 4 minutes?

Accepted Answer

$$C(4) = 50 \ln(5) \approx 80$$

Question 15

Which of the following is NOT a function?

Accepted Answer

A relation where the input $$x = 2 is $$paired with both $$y = 3$$ and $$y = 5$$

Question 16

If $$f(x) = x^2$ - 4x + 3$$, what are the zeros of $$f$$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 17

A student uses technology to evaluate $$\log_{10}(500). $$Which of the following is the correct decimal approximation?

Accepted Answer

$$\log_{10}(500) \approx 2.699$$

Question 18

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

Accepted Answer

All real numbers except $$0$$

Math 1111: College Algebra Course Description, Goals, and Student Learning Outcomes

Guida di studio - Domande di pratica

Study guide - Flashcard