Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![Domain - All x values for which a function is defined (input values)
Range - Possible y or Output values
(-3,-2)
EXAMPLE 1
DOMAIN AND RANGE
gmx)
(3,1)
a) Find Domain & Range of g(x),
The domain is the set of inputs East of the function
Input valves run a long the horizontal axis.
21. f(x)=3sin x
The furthest left hout valve associated with a pt. on the
graph is -3. The furthest right input values associated
with apt, on the graph is 3.
So Domain is
C-3,3], that is all reals from -3 to 3.
The range represents the set of output valves for the
function. Output valves run a long the vertical axis.
The lowest output valve of the function is 2. The
highest is 1. So the range is [-2, 1], all reals
frem -2
to 1.
EXAMPLE 2
Find the domain and range of f(x)=√√4-x²
Write answers in interval notation.
DOMAIN
For f(x) to be defined 4-x²20.
This is true when -2 ≤x≤2
Domain: [-2,2]
RANGE
The solution to a square root must always be
positive thus f(x) must be greater than or equal
to 0.
Range: [0,00)
Find the domain and range of each function. Write your answer in INTERVAL notation.
19. f(x)=x²-5
20. f(x)=√x+3
2
x-1
22. f(x)=-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d3d0313-ca74-43cf-98c7-55eac5c05caf%2Fc6311b05-d086-4a07-ab3d-772d674664c2%2F4nbv81_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Domain - All x values for which a function is defined (input values)
Range - Possible y or Output values
(-3,-2)
EXAMPLE 1
DOMAIN AND RANGE
gmx)
(3,1)
a) Find Domain & Range of g(x),
The domain is the set of inputs East of the function
Input valves run a long the horizontal axis.
21. f(x)=3sin x
The furthest left hout valve associated with a pt. on the
graph is -3. The furthest right input values associated
with apt, on the graph is 3.
So Domain is
C-3,3], that is all reals from -3 to 3.
The range represents the set of output valves for the
function. Output valves run a long the vertical axis.
The lowest output valve of the function is 2. The
highest is 1. So the range is [-2, 1], all reals
frem -2
to 1.
EXAMPLE 2
Find the domain and range of f(x)=√√4-x²
Write answers in interval notation.
DOMAIN
For f(x) to be defined 4-x²20.
This is true when -2 ≤x≤2
Domain: [-2,2]
RANGE
The solution to a square root must always be
positive thus f(x) must be greater than or equal
to 0.
Range: [0,00)
Find the domain and range of each function. Write your answer in INTERVAL notation.
19. f(x)=x²-5
20. f(x)=√x+3
2
x-1
22. f(x)=-
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