Applied Calculus, 7e (Hughes-Hallett)
Chapter 1 Functions and Change
1.1 What Is a Function?
1) f (x) is the age of Antarctic ice (in hundreds of years) at a depth of x meters below the
surface. increasing or decreasing?
Answer: increasing
Diff: 1 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
2) A graph of y = f (x) is given in the following figure.
A. What is f (5) (to the nearest whole number)?
B. What is the domain of the function?
Answer:
A. 0
B. 0 ≤ x ≤ 7
Diff: 1 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
1
,3) From the following table,
A. Find f (5)
B. Find the value(s) of x for which f (x) = 1. If there is more than one, list them in increasing
order, separated by commas.
x 1 2 3 4 5 6
f (x) 1 3 7 6 4 1
Answer:
A. 4
B. 1, 6
Diff: 2 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
4) Let y = f (x) = 2 - 5.
A. Find the value of y when x is zero.
B. Find f (3).
Answer:
A. -5
B. 13
Diff: 2 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
2
,5) The empirical function P = g(t) graphed below represents the population P of a city (in
thousands of people) at time t. The ________ of the function is from 1980 to 2020, and the
________ of the function is from approximately 35,000 to 70,000 people.
Answer: domain; range
Diff: 2 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
6) The graph of y = f (x) is shown in the following figure. The ________ of f (x) is
and the ________ of f (x) is
Answer: domain; range
Diff: 2 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
3
, 7) The graph of y = f (x) is shown in the following figure. Estimate f (1) (to the nearest
integer).
Answer: -5
Diff: 1 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
8) The graph of y = f (x) is shown in the following figure. Is the graph increasing or decreasing
around x = 3?
Answer: increasing
Diff: 1 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
4
Chapter 1 Functions and Change
1.1 What Is a Function?
1) f (x) is the age of Antarctic ice (in hundreds of years) at a depth of x meters below the
surface. increasing or decreasing?
Answer: increasing
Diff: 1 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
2) A graph of y = f (x) is given in the following figure.
A. What is f (5) (to the nearest whole number)?
B. What is the domain of the function?
Answer:
A. 0
B. 0 ≤ x ≤ 7
Diff: 1 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
1
,3) From the following table,
A. Find f (5)
B. Find the value(s) of x for which f (x) = 1. If there is more than one, list them in increasing
order, separated by commas.
x 1 2 3 4 5 6
f (x) 1 3 7 6 4 1
Answer:
A. 4
B. 1, 6
Diff: 2 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
4) Let y = f (x) = 2 - 5.
A. Find the value of y when x is zero.
B. Find f (3).
Answer:
A. -5
B. 13
Diff: 2 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
2
,5) The empirical function P = g(t) graphed below represents the population P of a city (in
thousands of people) at time t. The ________ of the function is from 1980 to 2020, and the
________ of the function is from approximately 35,000 to 70,000 people.
Answer: domain; range
Diff: 2 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
6) The graph of y = f (x) is shown in the following figure. The ________ of f (x) is
and the ________ of f (x) is
Answer: domain; range
Diff: 2 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
3
, 7) The graph of y = f (x) is shown in the following figure. Estimate f (1) (to the nearest
integer).
Answer: -5
Diff: 1 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
8) The graph of y = f (x) is shown in the following figure. Is the graph increasing or decreasing
around x = 3?
Answer: increasing
Diff: 1 Var: 1
Section: 1.1
Learning Objectives: Understand the properties and terminology of functions: input/output,
function notation, intercepts, increasing/decreasing.
4
