Q: Which of the following is an example of a piecewise function?

$$f(x) = \begin{cases} x^2$ & x \geq 0 \\ -x & x \u003c 0 \end{cases}$$

Question 1

Which of the following numbers has a non-terminating, non-repeating decimal expansion?

Accepted Answer

√2

Question 2

A hospital records the temperature of a patient every hour. Which of the following best describes the set of possible temperature readings?

Accepted Answer

Real numbers

Question 3

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

Accepted Answer

(-2, 5]

Question 4

Let $$A = \{x \mid 0 \u003c x \u003c 4\}$$ and $$B = \{x \mid 2 \u003c x \u003c 6\}. $$What is $$A \cap B$$?

Accepted Answer

\{x \mid 2 \u003c x \u003c 4\}

Question 5

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

Accepted Answer

$$x \geq 1$$

Question 6

Which of the following statements about rational and irrational numbers is TRUE?

Accepted Answer

Every rational number has a terminating or repeating decimal expansion.

Question 7

A company charges a flat fee of $$10 plus 2 $$per mile for delivery. Which of the following best represents the cost $$C as a $$function of miles $$m$$?

Accepted Answer

C(m) = 10 + 2m

Question 8

Which of the following graphs passes the vertical line test and thus represents a function?

Accepted Answer

A parabola opening upwards

Question 9

Suppose $$f(x) = \begin{cases} x^2$ & x \geq 0 \ -x & x \u003c 0 \end{cases}. $$What is $$f(-3)$$?

Accepted Answer

3

Question 10

If the distance between two points $$a$$ and $$b on $$the real number line is 7, which of the following could be true?

Accepted Answer

$$a = 2$$, $$b = 9$$

Question 11

Which of the following is NOT a function?

Accepted Answer

The rule assigning to each $$x$$ the value $$\pm\sqrt{x}$$ for $$x \geq 0$$

Question 12

A scientist measures the concentration of a chemical in a solution over time. Which mathematical concept best models the relationship between time and concentration?

Accepted Answer

A function

Question 13

Which of the following is the correct set-builder notation for the interval $$[2, 7)$$?

Accepted Answer

$$\{x \mid 2 \leq x \u003c 7\}$$

Question 14

If $$f(x) = \frac{1}{x-4}$$, what is the domain of $$f$$?

Accepted Answer

All real numbers except $$x = 4$$

Question 15

Which of the following statements is TRUE about the range of $$f(x) = x^2$?

Accepted Answer

The range is $$[0, \infty)$$

Question 16

A patient’s heart rate is measured every minute and recorded as a decimal. Which set best describes the possible values for the heart rate?

Accepted Answer

Real numbers

Question 17

Which of the following is an example of a piecewise function?

Accepted Answer

$$f(x) = \begin{cases} x^2$ & x \geq 0 \ -x & x \u003c 0 \end{cases}$$

Question 18

If $$A = \{x \mid x \u003e 1\}$$ and $$B = \{x \mid x \u003c 3\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{x \mid 1 \u003c x \u003c 3\}$$

Question 19

Which of the following best describes the set $$\mathbb{Q}$$?

Accepted Answer

The set of all rational numbers

Question 20

A car travels at a constant speed of 60 km/h. Which function describes the distance $$d (in km) $$after $$t$$ hours?

Accepted Answer

$$d = 60t$$

MATH 221: First Semester Calculus – Study Notes (Chapter 1: Numbers and Functions)

Study Guide - Practice Questions

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