Q: Suppose $$f(x) = x^2$. What is the domain and range of f$?

Domain: $$(-infty, infty)$$, Range: $$[0, infty)$$

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

$$f(x) = \begin{cases} x^2$ & x \u003c 0 \\ x+1 & x \\geq 0 \end{cases}$$

Question 1

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

Accepted Answer

$$(-2, 5]$$

Question 2

Suppose $$f(x) = x^2$. What is the domain and range of f$?

Accepted Answer

Domain: $$(-infty, infty)$$, Range: $$[0, infty)$$

Question 3

Which of the following numbers is NOT a rational number?

Accepted Answer

$$\sqrt{2}$$

Question 4

Given the function $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

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

Question 5

A function $$f$$ passes the vertical line test if and only if:

Accepted Answer

Every vertical line intersects the graph of $$f at $$most once.

Question 6

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 7

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

Accepted Answer

The slope of the line

Question 8

Which of the following intervals includes all real numbers $$x$$ such that $$x \geq 0$$?

Accepted Answer

$$[0, infty)$$

Question 9

A student claims that the decimal $$0.333... is a $$rational number. Is this correct, and if so, what is its fractional representation?

Accepted Answer

Yes, $$\frac{1}{3}$$

Question 10

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

Accepted Answer

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

Question 11

Suppose you are graphing $$y = f(x)$$ and want to indicate the domain of $$f. $$What does the domain represent?

Accepted Answer

The set of all $$x$$ values for which $$f(x) is $$defined

Question 12

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

Accepted Answer

$$f(x) = \begin{cases} x^2$ & x \u003c 0 \ x+1 & x \geq 0 \end{cases}$$

Question 13

If the graph of $$y = f(x)$$ fails the vertical line test, what does this mean?

Accepted Answer

The relation is not a function

Question 14

Which of the following is the correct set notation for all real numbers $$x$$ such that $$x \u003c 3$$?

Accepted Answer

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

Question 15

A real-world application: The distance $$d (in $$meters) an object falls in $$t$$ seconds under gravity (ignoring air resistance) is given by $$d = 4.9t^2$. What is the domain of this function?

Accepted Answer

$$[0, infty)$$

Question 16

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

Accepted Answer

A rule which assigns to each value in the domain exactly one value in the range

Question 17

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

Accepted Answer

$$[1, infty)$$

Question 18

Which of the following statements about the set $$\mathbb{Q} is $$true?

Accepted Answer

$$\mathbb{Q} is $$the set of all rational numbers

Question 19

A chemical reaction rate is modeled by $$R(t) = 2t + 5$$, where $$t is $$time in seconds. What does the slope of this function represent in the context of the reaction?

Accepted Answer

The rate at which the reaction rate increases per second

Numbers, Functions, and Foundations of Calculus

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