Q: Given the function $$f(x) = \dfrac{1}{x-2}$$, which of the following best describes its domain?

$$x \in \mathbb{R},\ x \neq 2$$

Q: Which of the following is the correct domain for $$f(x) = \dfrac{1}{x^2$ - 9}$$?

$$x \in \mathbb{R},\ x \neq 3,\ x \neq -3$$

Question 1

Given the function $$f(x) = \dfrac{1}{x-2}$$, which of the following best describes its domain?

Accepted Answer

$$x \in \mathbb{R},\ x 
eq 2$$

Question 2

A hospital monitors the temperature of a patient over time, modeled by $$T(t) = 98.6 + 0.5\sin(\pi t)$$, where $$t is in $$hours. What is the range of $$T(t)$$?

Accepted Answer

$$[98.1, 99.1]$$

Question 3

Which of the following functions is NOT one-to-one?

Accepted Answer

$$f(x) = x^2$

Question 4

A chemical reaction rate is modeled by $$R(t) = 5e$$^{-0.2t}$$, where t$ is time in minutes. What is the range of R(t$$)$$ for t$$ \geq 0$$?

Accepted Answer

$$(0, 5]$$

Question 5

Which of the following describes the domain of $$f(x) = \sqrt{3x - 6}$$?

Accepted Answer

$$x \geq 2$$

Question 6

A population of bacteria doubles every hour, modeled by $$P(t) = 100 \cdot 2^t. $$What is the population after 3 hours?

Accepted Answer

$$800$$

Question 7

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

Accepted Answer

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

Question 8

A medication's concentration in the bloodstream is modeled by $$C(t) = 50e$$^{-0.5t}$$, where t$ is in hours. After how many hours will the concentration drop to 10$ mg/L?

Accepted Answer

$$t = 3.22$$

Question 9

Which of the following functions has a range of $$(-\infty, 0)$$?

Accepted Answer

$$f(x) = -e^x$$

Question 10

A car's value depreciates according to $$V(t) = 20000(0.85)^t$$, where $$t is $$years since purchase. What is the value after 4 years?

Accepted Answer

$$10403$$

Question 11

Which of the following is the correct domain for $$f(x) = \dfrac{1}{x^2$ - 9}$$?

Accepted Answer

$$x \in \mathbb{R},\ x 
eq 3,\ x 
eq -3$$

Question 12

A scientist models the growth of a plant with $$h(t) = 2t^2$ + 3t + 1$$, where $$h is $$height in cm and $$t is $$days. What is the height after 5 days?

Accepted Answer

$$66 cm$$

Question 13

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 14

A radioactive substance decays according to $$A(t) = 1000e$$^{-0.1t}$$. What is the half-life of the substance?

Accepted Answer

$$t = 6.93$$

Question 15

Which of the following is the range of $$f(x) = \sqrt{x-4}$$?

Accepted Answer

$$[0, \infty)$$

Question 16

A company’s profit is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold. What is the maximum profit?

Accepted Answer

$$18$$

Question 17

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 18

A city’s population is modeled by $$P(t) = 5000 + 200t$$, where $$t is $$years since 2000. What will the population be in 2025?

Accepted Answer

$$10000$$

Question 19

Which of the following is the correct range for $$f(x) = \dfrac{1}{x}$$?

Accepted Answer

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

Question 20

A patient’s heart rate is modeled by $$H(t) = 70 + 10\cos(\pi t)$$, where $$t is in $$minutes. What is the maximum heart rate?

Accepted Answer

$$80$$

Functions: Domain and Range – Precalculus Study Notes

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