Q: If $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

All real numbers $$x$$ such that $$x \neq 2$$

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 $$x$$, that is $$(-\infty, \infty)$$

Question 3

A hospital uses the function $$C(t) = 500e$$^{0.04t}$$ to model the cost of a 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$

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 models its revenue with $$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 population growth with $$P(t) = 1000e$$^{0.03t}$$. If the population doubles, how many years will it take? (Round to the nearest year)

Accepted Answer

$$t = \frac{\ln 2}{0.03} \approx 23$$ years

Question 9

Which of the following graphs represents a function?

Accepted Answer

A graph that passes the vertical line test everywhere.

Question 10

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

Accepted Answer

$$x = 2, y = 1$$

Question 11

A pharmaceutical company uses the function $$Q(t) = 2000e$$^{-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

$$Q(10) = 2000e$$^{-0.5}$$ \approx 1213$$

Question 12

Which of the following is the solution to the inequality $$x^2 - 4x + 3$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 13

A car rental company charges $$C(x) = 40x + 25$$, where $$x is $$the number of days rented. If a customer has a budget of $$225$$, what is the maximum number of days they can rent the car?

Accepted Answer

$$x = 5$$

Question 14

Which of the following is the correct formula for the logarithmic function that is the inverse of $$f(x) = e$$^{2x}$$?

Accepted Answer

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

Question 15

A piecewise function is defined as $$f(x) = \begin{cases} x + 2 & x \u003c 0 \ 2x - 1 & x \geq 0 \end{cases}. $$What is $$f(-3)$$ and $$f(2)$$?

Accepted Answer

$$f(-3) = -1$$, $$f(2) = 3$$

Question 16

If $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

All real numbers $$x$$ such that $$x 
eq 2$$

Question 17

A scientist uses the function $$T(x) = 20 \log_{10}(x) to $$model the intensity of a sound in decibels, where $$x is $$the ratio of the sound's intensity to a reference level. If $$x = 100$$, what is $$T(x)$$?

Accepted Answer

$$T(100) = 40$$

Question 18

Which of the following best describes the range of the function $$f(x) = \ln(x)$$?

Accepted Answer

All real numbers $$(-\infty, \infty)$$

Question 19

A student uses technology to approximate $$\sqrt{50} to $$two decimal places. Which is the correct value?

Accepted Answer

$$\sqrt{50} \approx 7.07$$

College Algebra: Course Goals and Student Learning Outcomes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드