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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

(a) What is a function? What are its domain and range?

(b) What is the graph of a function?

(c) How can you tell whether a given curve is the graph of a function?

(a)

To determine

To explain: The terms function, domain of a function and range of a function.

Explanation

A function f is defined as a ordered pair (x,f(x)) such that x and f(x) are related by a definite rule.

The set of all such values of x is domain D for the function f and the set of all values of f(x) is called as range R.

(b)

To determine

To explain: The meaning of graph of the function f.

Explanation

Graph:

Draw the graph of the function f as shown in the Figure1

images

As per the definition of the function it is an ordered pair (x,f(x)).

Plot the point (x,f(x))=(x,y) in the xy-plane for all values of x in the domain.

Connect all the points to obtain a curve this curve is known as graph of the function f.

(c)

To determine

To check: Whether the graph of a function exists or not.

Explanation

If the graph has no vertical line intersects to the curve more than once, then the graph of a function exists.

If the graph has the vertical line intersect to the curve more than once, then the graph of a function does not exist

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