Question 1

Which of the following statements best describes the purpose of calculus?

Accepted Answer

Calculus deals with finding rates of change (derivatives) and areas, lengths, and volumes (integrals).

Question 2

Given the function $$f(x) = |x|$$, which of the following is true about its graph?

Accepted Answer

It is a V-shaped graph symmetric about the y-axis.

Question 3

Which of the following sets includes all rational numbers?

Accepted Answer

$$\mathbb{Q} ($$rational numbers)

Question 4

A function $$f(x) is $$called even if:

Accepted Answer

$$f(x) = f(-x)$$

Question 5

Which of the following is the correct difference quotient for the function $$f(x)$$?

Accepted Answer

$$\dfrac{f(x+h) - f(x)}{h}$$

Question 6

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of f(g(x$$))$$?

Accepted Answer

$$x \geq 0$$

Question 7

Which of the following intervals represents the solution to the compound inequality $$x  2$$?

Accepted Answer

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

Question 8

A vertical line has which of the following equations?

Accepted Answer

$$x = a$$

Question 9

Which function is an example of an odd power function?

Accepted Answer

$$f(x) = x^3$

Question 10

If $$f(x) = x^2$ and g(x) = x + 1$, what is f(g(x$$))$$?

Accepted Answer

$$(x + 1)^2$

Question 11

Which of the following is NOT a transcendental function?

Accepted Answer

$$f(x) = x^2$

Question 12

The vertical line test is used to determine if a graph represents a function. Which statement is correct?

Accepted Answer

If a vertical line intersects the graph only once everywhere, it is a function.

Question 13

Which of the following describes an increasing function?

Accepted Answer

A function that never decreases and may stop for a while.

Question 14

Given $$f(x) = x^2$ and g(x$$) = $$x^3$$, which of the following is $$f(x) + g(x)$$?

Accepted Answer

$$x^2$$ + $$x^3$$

Question 15

Which of the following is the correct point-slope form of a line passing through $$(x_1$, y_1$)$$ with slope $$m$$?

Accepted Answer

$$y = m(x - x_1$) + y_1$

Question 16

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

Accepted Answer

$$x \geq 0$$

Question 17

Which of the following is the correct intercept form of a line with x-intercept $$a$$ and y-intercept $$b$$?

Accepted Answer

$$\dfrac{x}{a} + \dfrac{y}{b} = 1$$

Question 18

Which of the following is the correct expression for the absolute value function?

Accepted Answer

$$f(x) = |x|$$

Question 19

If $$f(x) = x^2$ and g(x$$) = $$x^3$$, what is $$f(g(x))$$?

Accepted Answer

$$(x^3)^2$

Foundations of Calculus: Functions, Domains, and Graphs

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