Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(0,1), (2,3), (4,5), (6,7)\}$$

Question 2

Given the graph in image 2, does it represent a function? Use the vertical line test to justify your answer.

Accepted Answer

Yes, because every vertical line intersects the graph at most once.

Question 3

What is the domain of the function $$f(x) = \sqrt{3-x^2$}$$?

Accepted Answer

$$[-\sqrt{3}, \sqrt{3}]$$

Question 4

Classify the function $$f(x) = \frac{x^2$-1}{x+2}$$ and state its domain.

Accepted Answer

Rational; domain is $$(-\infty, -2) \cup (-2, \infty)$$

Question 5

Evaluate $$f(-3)$$ for the piecewise function in image 3.

Accepted Answer

$$-2(-3)-1 = 5$$

Question 6

For the function $$f(x) = x^2$ + 1$$, what is $$f(5)$$?

Accepted Answer

$$26$$

Question 7

Which of the following best describes the domain of a polynomial function?

Accepted Answer

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

Question 8

Given $$f(x) = \sqrt{5x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$[\frac{1}{5}, \infty)$$

Question 9

Evaluate $$f(2)$$ for the piecewise function in image 3.

Accepted Answer

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

Question 10

If $$f(x) = x^2$ - 3x$$, calculate and simplify $$\frac{f(x+h)-f(x)}{h}.$$

Accepted Answer

$$2x - 3 + h$$

Question 11

Which of the following is NOT a function?

Accepted Answer

$$y^2 = x$

Question 12

Given $$f(x) = 2x^2$ + 7$$, calculate and simplify $$\frac{f(x+h)-f(x)}{h}.$$

Accepted Answer

$$4x + 2h$$

Question 13

For the function $$f(x) = \sqrt{x} - 3x$$, find $$f(4).$$

Accepted Answer

$$2 - 12 = -10$$

Question 14

Which of the following describes the domain of $$f(x) = \frac{1}{x-5}$$?

Accepted Answer

$$(-\infty, 5) \cup (5, \infty)$$

Question 15

Evaluate $$f(0)$$ for the piecewise function $$f(x) = \begin{cases} 3x+5 & x\u003c0 \ x+7 & x \geq 0 \end{cases}.$$

Accepted Answer

$$7$$

Question 16

If $$f(x) = x^2$ + 2$$, what is the value of $$f(-4)$$?

Accepted Answer

$$18$$

Question 17

Given $$f(x) = -3x + 5$$, evaluate $$f(7).$$

Accepted Answer

$$-16$$

Question 18

For the function $$f(x) = \sqrt[3]{x-1}$$, what is the domain?

Accepted Answer

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

Question 19

Which of the following is the correct function notation for 'y equals x squared plus 2'?

Accepted Answer

$$f(x) = x^2$ + 2$$

Relations, Functions, and Piecewise Functions – Study Notes

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