Question 1

Which of the following best describes a function?

Accepted Answer

A relation in which each element of the domain is paired with exactly one element of the range.

Question 2

Given the relation $$\{(2,5), (3,7), (2,8)\}$$, is this relation a function? Why or why not?

Accepted Answer

No, because the input 2 is paired with two different outputs.

Question 3

Which of the following equations defines $$y as a $$function of $$x$$?

Accepted Answer

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

Question 4

If $$f(x) = 2x^2$ - 5x$$, what is $$f(-1)$$?

Accepted Answer

$$7$$

Question 5

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

Accepted Answer

$$[2, \infty)$$

Question 6

Which of the following is the explicit form of the equation $$2x - y = 4$$?

Accepted Answer

$$y = 2x - 4$$

Question 7

If $$f(x) = \frac{3x}{x-2}$$, what values must be excluded from the domain?

Accepted Answer

$$x = 2$$

Question 8

Given $$f(x) = x^2$ - 2$$ and $$h 
eq 0$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h$$

Question 9

Suppose $$f(x) = \sqrt{x-7}$$ and $$g(x) = x+2. $$What is the domain of $$f(g(x))$$?

Accepted Answer

$$[5, \infty)$$

Question 10

If $$f(x) = 2x^2$ - 5x$$ and $$g(x) = x+1$$, what is $$(f+g)(x)$$?

Accepted Answer

$$2x^2 - 4x + 1$

Question 11

Which of the following is NOT a valid way to represent a relation?

Accepted Answer

As a polynomial equation

Question 12

Given $$f(x) = \frac{x+5}{x-3}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 13

If $$f(x) = x^2$ and g(x) = x+1$, what is (f$$ \cdot g)(x)$$?

Accepted Answer

$$x^2(x+1$$)$$

Question 14

Which of the following real-world scenarios can be modeled by a function?

Accepted Answer

Assigning each person in a class to their unique student ID number.

Question 15

Given $$f(x) = \sqrt{x}$$, which of the following is true about its domain?

Accepted Answer

$$x \geq 0$$

Question 16

If $$f(x) = 2x^2$ - 5x$$ and $$g(x) = x+1$$, what is $$(f-g)(x)$$?

Accepted Answer

$$2x^2 - 6x - 1$

Question 17

Which of the following is the correct difference quotient for $$f(x) = 3x$$?

Accepted Answer

$$3$$

Question 18

If $$f(x) = \frac{1}{x}$$ and $$g(x) = \frac{x}{x+3}$$, what is the domain of $$(f \cdot g)(x)$$?

Accepted Answer

$$x 
eq 0, x 
eq -3$$

Question 19

Which of the following best describes the vertical line test for functions?

Accepted Answer

A graph represents a function if and only if no vertical line intersects the graph at more than one point.

Question 20

Given $$f(x) = \sqrt{x-2}$$ and $$g(x) = x^2$, what is the domain of f(g(x$$))$$?

Accepted Answer

$$(-\infty, -\sqrt{2}] \cup [\sqrt{2}, \infty)$$

Functions and Their Graphs: Precalculus Study Notes

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