Chapter EP, Problem 2.1.8EP

To determine

To Find: The graph for each of the equation and determine the domain and the range. Also, determine whether the equation is the function is one to one onto both or neither and state whether it is discrete or continuous.

Answer to Problem 2.1.8EP

Thegraph is shown in Figure 1 the domain of the equation is

  $\left\{-2,-1,0,1,2\right\}$ and the range is $\left\{0,2,8\right\}$ , the equation is one to one function and it is continuous.

Explanation of Solution

Given:

The equation is $y=2x^2$ .

Calculation:

Consider the given equation is,

  $y=2x^2$

Table for the value of $y$ for different value of $x$ is shown in Table 1

Table 1

$x$	$y=-x^2$
$-2$	8
$-1$	2
0	0
1	2
2	8

The domain of the equation is,

  $\left\{-2,-1,0,1,2\right\}$

The range of the equation is,

  $\left\{0,2,8\right\}$

Since, each value of the domain is paired with exactly one value of the range so the relation is a function.

The graph for the above equation is shown in Figure 1

Figure 1

Since $x$ can be any real number so there are an infinite number of ordered pairs that can be graphed

It is seen that for every real number is the x coordinate of some point on the line. Thus, for every real number is the y coordinate of some point on the line.

The domain and range are both the real numbers thus the relation is continuous.