Question 1

Which of the following relations is a function?

Accepted Answer

The relation $$\{(3,6), (6,9), (9,12)\}$$

Question 2

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

Accepted Answer

$$-4$$

Question 3

Which of the following equations does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 4

A rock is dropped from a height of $$80$$ meters. The height $$H (in $$meters) after $$t$$ seconds is approximately $$H(t) = 80 - 4.9t^2$. What is the height after 3$ seconds?

Accepted Answer

$$26.9$$ meters

Question 5

Find the domain of the function $$g(x) = \frac{3x}{x^2$ - 81}.$$

Accepted Answer

All real numbers except $$x = 9$$ and $$x = -9$$

Question 6

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

Accepted Answer

$$x \geq 2$$

Question 7

Given $$f(x) = x^2$ + 3x - 1$$ and $$g(x) = 2x - 5$$, find $$(f + g)(x).$$

Accepted Answer

$$x^2 + 5x - 6$

Question 8

Which of the following is the range of the relation $$\{(4, 8.888), (5.488, -5.5), (7, 2.33), (9, -4)\}$$?

Accepted Answer

$$\{8.888, -5.5, 2.33, -4\}$$

Question 9

If $$f(x) = |x| + 4$$, what is $$f(-3)$$?

Accepted Answer

$$7$$

Question 10

Given $$f(x) = \frac{2x - 4}{x + 7}$$, find $$f(1).$$

Accepted Answer

$$-\frac{2}{8}$$

Question 11

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\frac{(x + h)^2$ - x^2$}{h}$$

Question 12

If $$f(x) = \sqrt{x + 9}$$, what is $$f(-5)$$?

Accepted Answer

$$\sqrt{4}$$

Question 13

Given $$f(x) = x^2$ - 2x + 1$$, what is $$f(3)$$?

Accepted Answer

$$1$$

Question 14

Which of the following is the domain of $$f(x) = \frac{1}{x^2$ - 6x}$$?

Accepted Answer

All real numbers except $$x = 0$$ and $$x = 6$$

Question 15

If $$f(x) = 2x^2$ - 6x + 7$$, what is $$f(4)$$?

Accepted Answer

$$15$$

Question 16

Given $$f(x) = \sqrt{x - 2}$$, what is $$f(6)$$?

Accepted Answer

$$\sqrt{4}$$

Question 17

Which of the following is NOT a function?

Accepted Answer

A relation where an input is paired with multiple outputs

Question 18

If $$f(x) = x^2$ + 3x - 1$$ and $$g(x) = 2x - 5$$, find $$(f - g)(x).$$

Accepted Answer

$$x^2 + x + 4$

Question 19

A medical researcher models the temperature $$T (in$$ °C) of a patient over time $$t (in $$hours) as $$T(t) = 37 + 0.5t - 0.1t^2$. What is the temperature after 4$ hours?

Accepted Answer

$$37.4$$ °C

Functions and Their Properties: Precalculus Study Notes

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