Chapter 1, Problem 1RCC

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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

The set of all such values of *x* is domain *D* for the function *f* and the set of all values of *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

As per the definition of the function it is an ordered pair

Plot the point *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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