Chapter 1, Problem 38CR

To determine

To Find: whether $y$ is a function of $x$ for the equation $\left|x+5\right|-2y=0$ using vertical line test and describe how graph can be drawn using graphing utility.

Answer to Problem 38CR

  $y$ is a function of $x$ .

Explanation of Solution

Given Given equation is $\left|x+5\right|-2y=0$ and graph is show below .

  

Calculation:

Vertical line test is used to determine whether a graph represents a function. If a vertical line is drawn that intersects a graph more than once, then the graph does not indicate a function because a function always has only one value of function for one value of x .

Drawing a vertical line cutting the graph as shown below.

  

The vertical line cuts the graph at a single point therefore $y$ is a function of $x$ .

The above graph is drawn using graphic calculator for given coordinates.

  $\begin{array}{l}\left|x+5\right|-2y=0\\ 2y=\left|x+5\right|\\ y=\frac{1}{2}\left|x+5\right|\\ y=\pm \frac{\left(x+5\right)}{2}\end{array}$

For $y=\frac{\left(x+5\right)}{2}$ ,the coordinates are.

  $\begin{array}{cc}x& y\\ 0& 2.5\\ -5& 0\end{array}$

For $y=-\frac{\left(x+5\right)}{2}$ ,the coordinates are.

  $\begin{array}{cc}x& y\\ 0& -2.5\\ -5& 0\end{array}$

Since, it is a modulus function therefore value of y will always be positive.

Therefore, graph can be drawn using above coordinates.

So, $y$ is a function of $x$ .