Q: Given the equation $$y = -2x + 10$$, rewrite it in function notation and evaluate $$f(3).$$

$$f(3) = -2 \times 3 + 10 = 4$$

Question 1

Which of the following relations is a function?

Accepted Answer

$$\{(2, 5), (0, 2), (3, 9)\}$$

Question 2

Given the equation $$y = -2x + 10$$, rewrite it in function notation and evaluate $$f(3).$$

Accepted Answer

$$f(3) = -2 	imes 3 + 10 = 4$$

Question 3

Which graph passes the vertical line test and represents a function?

Accepted Answer

A graph of a parabola opening upwards

Question 4

What is the domain of the function $$f(x) = \sqrt{x + 4}$$? Express your answer in interval notation.

Accepted Answer

$$[-4, \infty)$$

Question 5

Find the domain of $$f(x) = \dfrac{1}{x^2$ - 5x + 6}. $$Express your answer in interval notation.

Accepted Answer

$$(-\infty, 2) \cup (2, 3) \cup (3, \infty)$$

Question 6

Which of the following equations is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 25$

Question 7

Given the graph of $$f(x)$$ with domain $$[-4, 0) \cup [1, 4]$$ and range $$(-3, 1] \cup [1, 3]$$, which of the following is true?

Accepted Answer

The function is not defined for $$x$$ between $$0$$ and $$1$$

Question 8

A chemical reaction's temperature $$T (in$$ $$^\circC) is $$modeled by $$T(t) = 5t + 20$$, where $$t is $$time in minutes. What is the temperature after 8 minutes?

Accepted Answer

$$T(8) = 60$$ $$^\circC$$

Question 9

Which of the following statements about functions is correct?

Accepted Answer

A function assigns exactly one output to each input

Question 10

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

Accepted Answer

$$[0, \infty)$$

Question 11

A hospital monitors a patient's heart rate $$H(t)$$, modeled by $$H(t) = 70 + 5t$$ for $$0 \leq t \leq 10. $$What is the domain of $$H$$?

Accepted Answer

$$[0, 10]$$

Question 12

Which interval notation correctly represents all real numbers except $$x = 5$$?

Accepted Answer

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

Question 13

Given $$f(x) = \dfrac{1}{x-2}$$, which value is NOT in the domain?

Accepted Answer

$$x = 2$$

Question 14

A relation is given by the set $$\{(1, 2), (2, 3), (1, 4)\}. Is $$this a function?

Accepted Answer

No, because input $$1$$ has two different outputs

Question 15

Which of the following is the correct set builder notation for the domain $$[1, 5]$$?

Accepted Answer

$$\{x | 1 \leq x \leq 5\}$$

Question 16

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

Accepted Answer

$$[-4, \infty)$$

Question 17

Which of the following equations will always pass the vertical line test?

Accepted Answer

$$y = 2x + 1$$

Question 18

A function $$f is $$defined by $$f(x) = \sqrt{x-1}. $$What is the domain of $$f$$?

Accepted Answer

$$[1, \infty)$$

Question 19

Which of the following is NOT a valid way to express the range of a function?

Accepted Answer

Using $$x$$ values only

Question 20

If $$f(x) = \dfrac{1}{x^2$}$$, what is the domain of $$f$$?

Accepted Answer

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

Relations, Functions, Domain, and Range: College Algebra Study Notes

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