Question 1

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

All real numbers except $$x = 2$$

Question 2

Given the function $$f(x) = x^2$ + 3x - 4$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 3

Which of the following is NOT a function?

Accepted Answer

A relation where some inputs have more than one output

Question 4

Evaluate $$f(3)$$ for the function $$f(x) = 2x^2$ - x + 5.$$

Accepted Answer

$$16$$

Question 5

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

Accepted Answer

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

Question 6

A hospital monitors the temperature of a patient over time, modeled by $$T(t) = 98.6 + 0.5\sin(\frac{\pi t}{12}). $$What is the period of this function?

Accepted Answer

$$24$$

Question 7

Which of the following is a polynomial function?

Accepted Answer

$$f(x) = x^3$ - 2x + 5$$

Question 8

If $$g(x) = x^2$ and h(x) = 3x + 1$, what is (g$$ \circ h)(x)$$?

Accepted Answer

$$(3x + 1)^2$

Question 9

Which of the following graphs represents an even function?

Accepted Answer

A graph symmetric about the y-axis

Question 10

A population of bacteria doubles every hour. If the initial population is $$P_0$$, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = P_0$ \cdot 2^t$$

Question 11

Which of the following is the correct formula for the sine of a sum, $$\sin(a + b)$$?

Accepted Answer

$$\sin(a + b) = \sin a \cos b + \cos a \sin b$$

Question 12

Which function has a vertical asymptote at $$x = 0$$?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 13

Which of the following is the correct graph for $$f(x) = |x|$$?

Accepted Answer

A V-shaped graph opening upwards

Question 14

If $$f(x) is an $$odd function, which of the following must be true?

Accepted Answer

$$f(-x) = -f(x)$$

Question 15

Which of the following is the correct formula for the cosine of a difference, $$\cos(a - b)$$?

Accepted Answer

$$\cos(a - b) = \cos a \cos b + \sin a \sin b$$

Question 16

A ball is thrown upward and its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 64t + 80. $$What is the maximum height reached by the ball?

Accepted Answer

$$208$$

Question 17

Which of the following is the correct formula for the period of the function $$f(x) = \sin(kx)$$?

Accepted Answer

$$\frac{2\pi}{k}$$

Question 18

Which of the following is a real-world example of an exponential function?

Accepted Answer

The amount of money in a bank account growing with compound interest

Question 19

Which of the following is the correct formula for the graph of a quadratic function?

Accepted Answer

$$y = ax^2$ + bx + c$$

Question 20

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

Accepted Answer

A rule that assigns each element in the domain to exactly one element in the range

Calculus Study Guide: Functions and Their Properties

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