2
Applied Calculus, 7th Edition By Deborah Hughes-Hallett
Email: richard@qwconsultancy.com
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 f (x)
1 1
2 3
3 7
4 6
5 4
6 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