$$\\\\mathbb{R} ($$all real numbers)

$$f'(a) = \\\\lim_{h \\\\to 0} \\\\frac{f(a+h) - f(a)}{h}$$

$$\\\\mathbb{R} ($$all real numbers)

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

Question 1

Which of the following sets contains all real numbers $$x$$ such that $$x^2$$ \u003c 4$$?

Accepted Answer

$$(-2, 2)$$

Question 2

Suppose $$f(x) = x^2$ + 1. $$What is the domain of $$f$$?

Accepted Answer

$$\\mathbb{R} ($$all real numbers)

Question 3

Which of the following functions is NOT continuous for all real numbers?

Accepted Answer

$$f(x) = \\frac{1}{x}$$

Question 4

Given the function $$f(x) = \\sqrt{x-3}$$, what is its domain?

Accepted Answer

$$[3, \\infty)$$

Question 5

If $$f(x) = 2x + 5$$ and $$g(x) = x^2$, what is (f$$ \\circ g)(x)$$?

Accepted Answer

$$2x^2 + 5$

Question 6

Which of the following is the correct definition of the derivative of $$f(x) at$$ $$x=a$$?

Accepted Answer

$$f'(a) = \\lim_{h \\to 0} \\frac{f(a+h) - f(a)}{h}$$

Question 7

A car's position at time $$t is $$given by $$s(t) = 4t^2$ + 2t. $$What is the instantaneous velocity at $$t = 3$$?

Accepted Answer

$$26$$

Question 8

Which of the following statements about the graph of a function is TRUE?

Accepted Answer

The domain of a function is the set of all $$x-$$values for which the function is defined.

Question 9

If $$f(x) = x^2$ and g(x) = x + 1$, what is the domain of (f$$ \\circ g)(x)$$?

Accepted Answer

$$\\mathbb{R} ($$all real numbers)

Question 10

Which of the following is a correct interpretation of the vertical line test?

Accepted Answer

A graph represents a function if and only if no vertical line intersects the graph at more than one point.

Question 11

Let $$f(x) = \\frac{1}{x-2}. $$What is the range of $$f$$?

Accepted Answer

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

Question 12

Which of the following is the correct set notation for all real numbers $$x$$ such that $$x \\geq 5$$?

Accepted Answer

$$[5, \\infty)$$

Question 13

A function $$f is $$defined by $$f(x) = \\sqrt{9 - x^2$}. $$What is the domain of $$f$$?

Accepted Answer

$$[-3, 3]$$

Question 14

Which of the following is a rational number?

Accepted Answer

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

Question 15

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

Accepted Answer

$$x^2 + 2x$

Question 16

Which of the following intervals contains all real numbers $$x$$ such that $$-1 \u003c x \\leq 4$$?

Accepted Answer

$$(-1, 4]$$

Question 17

Suppose $$f(x) = x^2$ and g(x) = x + 2$. What is f(g(3$$))$$?

Accepted Answer

$$25$$

Question 18

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

Accepted Answer

$$|a - b|$$

Question 19

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

Accepted Answer

A rule which tells you how to compute the value $$f(x) of $$the function for a given real number $$x.$$

Calculus I Study Notes: Numbers, Functions, and Graphs

Study Guide - Practice Questions