Question 1

Which of the following sets contains all real numbers $$x$$ such that $$-1 \u003c x \u003c 6$$?

Accepted Answer

$$B = \{x \mid -1 \u003c x \u003c 6\}$$

Question 2

Which of the following functions has a finite decimal expansion?

Accepted Answer

$$\frac{1}{4}$$

Question 3

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

Accepted Answer

$$x \geq 2$$

Question 4

A function $$f is $$defined by $$f(x) = \frac{1}{x-3}. $$What is the domain of $$f$$?

Accepted Answer

$$x 
eq 3$$

Question 5

Which of the following best describes the range of the function $$f(x) = x^2$ for x$ in $$\mathbb{R}$$?

Accepted Answer

$$[0, \infty)$$

Question 6

Suppose you are asked to graph the function $$y = x^2$. Which property must the graph satisfy to be a function?

Accepted Answer

It must pass the vertical line test.

Question 7

Which of the following is the correct formula for the distance between two real numbers $$a$$ and $$b on $$the number line?

Accepted Answer

$$|a-b|$$

Question 8

If $$f(x) = mx + b is a $$linear function, what does the constant $$m$$ represent?

Accepted Answer

The slope of the line

Question 9

Which of the following intervals includes all real numbers $$x$$ such that $$2 \leq x \u003c 5$$?

Accepted Answer

$$[2, 5)$$

Question 10

A real-world application: The distance $$d$$ between two cars on a straight road is given by $$d = |x_1$ - x_2$|$$, where $$x_1$$ and $$x_2$$ are their positions. If car A is at $$x_1 = 120$ meters and car B is at x_2$ = 85$$ meters, what is the distance between them?

Accepted Answer

$$35$$ meters

Question 11

Which of the following sets is the solution to $$x^2 = 4$?

Accepted Answer

$$\{-2, 2\}$$

Question 12

Consider the function $$f(x) = \frac{1}{x}. $$Which value of $$x is $$not in the domain of $$f$$?

Accepted Answer

$$x = 0$$

Question 13

Which of the following is NOT a function?

Accepted Answer

A relation where some $$x$$ values are paired with more than one $$y$$ value

Question 14

If the graph of a relation fails the vertical line test, what does this indicate?

Accepted Answer

The relation is not a function

Question 15

Which of the following is the correct set notation for the set of all real numbers except $$0$$?

Accepted Answer

$$\mathbb{R} \setminus \{0\}$$

Question 16

Suppose $$f(x) = \sqrt{x} is $$defined for $$x \geq 0. $$What is the range of $$f$$?

Accepted Answer

$$[0, \infty)$$

Question 17

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

Accepted Answer

A rule which assigns to each $$x in $$the domain exactly one $$y$$ value

Question 18

If $$f(x) = 2x + 5$$, what is $$f(3)$$?

Accepted Answer

$$11$$

Question 19

Which of the following is the correct interval notation for all real numbers $$x$$ such that $$x \u003e 0$$?

Accepted Answer

$$(0, \infty)$$

Question 20

A medical thermometer measures temperature $$T in $$degrees Celsius. If the normal human body temperature is $$T = 37$$, which of the following intervals best describes the set of temperatures considered 'normal' if normal is defined as $$36 \leq T \leq 37.5$$?

Accepted Answer

$$[36, 37.5]$$

MATH 221 First Semester Calculus: Numbers, Functions, and Foundations

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