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?

To determine

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

Explanation of Solution

A function f is defined as a ordered pair $\left(x,f\left(x\right)\right)$ such that $x\text{ and }f\left(x\right)$ 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 $f\left(x\right)$ is called as range R.

To determine

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

Explanation of Solution

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 $\left(x,f\left(x\right)\right)$.

Plot the point $\left(x,f\left(x\right)\right)=\left(x,y\right)$ 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.

To determine

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

Explanation of Solution

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