Chapter 8.2, Problem 42E

a.

To determine

To complete:

The given table using given equation.

Answer to Problem 42E

The complete table would be:

x	$-3$	$-2$	$-1$	0	1	2	3
y	9	4	1	0	1	4	9

Explanation of Solution

Given:

An equation and a table:

  $y=x^2$ .

x	$-3$	$-2$	$-1$	0	1	2	3
y

Calculation:

To complete our given table, we will substitute the given values of xin our given equation as:

  $\begin{array}{l}y=x^2\\ $ y={(-3)}^2$y=9\end{array}$

  $\begin{array}{l}y=x^2\\ $ y={(-2)}^2$y=4\end{array}$

  $\begin{array}{l}y=x^2\\ $ y={(-1)}^2$y=1\end{array}$

  $\begin{array}{l}y=x^2\\ y=0^2\\ y=0\end{array}$

  $\begin{array}{l}y=x^2\\ y=1^2\\ y=1\end{array}$

  $\begin{array}{l}y=x^2\\ y=2^2\\ y=4\end{array}$

  $\begin{array}{l}y=x^2\\ y=3^2\\ y=9\end{array}$

Therefore, the complete table would be:

x	$-3$	$-2$	$-1$	0	1	2	3
y	9	4	1	0	1	4	9

b.

To determine

To graph:

The equation $y=x^2$ using the table and drawing a smooth curve that passes through all points.

Answer to Problem 42E

The graph of the equation $y=x^2$ would look like:

Explanation of Solution

Given:

An equation: $y=x^2$

Calculation:

Upon graphing our given equation, we will get our required graph as shown below:

c.

To determine

Is $y=x^2$ a linear equation? Is $y=x^2$ a function? Explain.

Answer to Problem 42E

No, the equation $y=x^2$ is not a linear equation.

Yes, the equation $y=x^2$ is a function.

Explanation of Solution

Given:

An equation: $y=x^2$

Calculation:

We know that the graph of a linear equation is a straight line. Since the graph of our given equation is not a straight line, therefore, the equation $y=x^2$ is not a linear equation.

We can see from our graph that each value of x corresponds to a specific y -value and there is only one output for each input. Therefore, the equation $y=x^2$ is a function.