Chapter 1, Problem 1CC

(a)

To determine

To Explain: about the function, its domain and rang.

Explanation of Solution

Given information:

Consider the function

The function is a relation defined on two sets, that is every element of first set contains a

unique element in second set.

Domain of the function is the set of all possible input values of a function.

Range of the function is the set of possible outputs.

Consider the function $f(x)=x^2$

Domain is the possible x values, here $(-\infty ,\infty )$ .

Range is the $f(x)$ values for which x values the function is defined. Here $(-\infty ,\infty )$ .

(b)

To determine

To Explain: about the graph of the function

Explanation of Solution

Given information:

Consider the graph of the function.

Consider the function $f(x).$

The domain values are o the $x-$ axis.

The range values are in the $y-$ axis.

The graph of the function is set of all points in the plane of the form $(x,f(x))$

(c)

To determine

To Explain: the method to identify weather the given curve is a graph of a function.

Explanation of Solution

Given information:

Consider the graph of the function.

Vertical line test is used to verify weather the given curve is a function or not.

According to vertical line test,

Draw a vertical line on to the given curve, if the vertical line intersect the curve at only

once, then the curve is a graph of the function, otherwise not.