Question 1

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

Accepted Answer

$$\{x \mid 1 \u003c x \u003c 6\}$$

Question 2

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

Accepted Answer

$$x \geq 2$$

Question 3

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 value $$f(x).$$

Question 4

Suppose you are graphing the function $$y = x^2$. Which of the following statements about its domain and range is correct?

Accepted Answer

Domain: all real numbers; Range: $$y \geq 0$$

Question 5

A straight line has the equation $$y = mx + b. $$What does the parameter $$m$$ represent?

Accepted Answer

The slope of the line

Question 6

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

Accepted Answer

$$[-2, 5)$$

Question 7

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

Accepted Answer

All real numbers except $$x = 0$$

Question 8

Which of the following is a rational number?

Accepted Answer

$$\frac{7}{3}$$

Question 9

A function $$f is $$defined by $$f(x) = x^2$ - 4x + 3. $$What is the value of $$f(2)$$?

Accepted Answer

$$-1$$

Question 10

Which of the following best describes the range of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

All real numbers $$y \geq 0$$

Question 11

If the distance between two numbers $$a$$ and $$b on $$the real number line is $$|a-b|$$, what is the distance between $$-3$$ and $$5$$?

Accepted Answer

$$8$$

Question 12

Which of the following is NOT a function?

Accepted Answer

A rule that assigns to each $$x in $$the domain more than one value $$f(x)$$

Question 13

Which of the following is the correct set notation for the set of all $$x$$ such that $$x is a $$rational number?

Accepted Answer

$$\mathbb{Q}$$

Question 14

If $$f(x) = 2x + 1$$, what is the slope of the graph of $$f$$?

Accepted Answer

$$2$$

Question 15

Which of the following is the correct interval notation for all real numbers $$x$$ such that $$x \u003e 3$$?

Accepted Answer

$$(3, \infty)$$

Question 16

Suppose $$f(x) = x^2$ and g(x) = x + 1$. What is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 17

Which of the following is an example of a finite decimal expansion?

Accepted Answer

$$0.25$$

Question 18

If $$f(x) = x^2$ and f(a) = 16$, what is a$?

Accepted Answer

$$a = 4 or$$ $$a = -4$$

Question 19

Which of the following best describes the set $$\{x \mid x^2$ = 4\}$$?

Accepted Answer

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

Question 20

A real-world application: The distance $$d in $$meters that a car travels in $$t$$ seconds is given by $$d(t) = 20t. $$How far does the car travel in 3 seconds?

Accepted Answer

$$60$$ meters

Numbers, Functions, and Foundations of Calculus

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