Chapter 1.9, Problem 74E

To determine

Graph the equation with the help of graphing calculator

Answer to Problem 74E

Explanation of Solution

Given information:

Write a short essay describing different ways in which a graphing calculator might give a misleading graph of an equation.

Calculation:

A graphing calculator displays a rectangular portion of the graph of an equation in a display window or viewing screen, which we call a viewing rectangle. The default screen often gives an incomplete or misleading picture, so it is important to coose the viewing rectangle with care.

Let us graph the equation $y=x^2+3$ with different viewing rectangles. We start with the viewing rectangle $\left[-2,2\right]by\left[-2,2\right]$ . The resulting graph as shown below is blank.

  

This is because for all $x$ ,

  $\begin{array}{l}{x}^2\ge 0\\ x^2+3\ge 3\end{array}$

Hence, the graph lies entirely above the viewing rectangle, so this viewing rectangle is not appropriate.

If we enlarge the viewing rectangle to $\left[-4,4\right]by\left[-4,4\right]$ , as illustrated below, we begin to see a portion of the graph.

  

If we enlarge the viewing rectangle to $\left[-10,10\right]by\left[-5,30\right]$ , the graph seems to be more complete.

  

Further enlarging the viewing rectangle, the graph do not show the $y-$ intercept is $3$ .

  

Hence, the viewing rectangle to $\left[-10,10\right]by\left[-5,30\right]$ is an appropriate representation of the graph.

Now graph the equations $y=3x^2-6+1\&y=0.23x-2.25$ together in the viewing rectangle $\left[-1,3\right]by\left[-2.5,1.5\right]$ . The graphs are so shown below.

  

One is a parabola, while the other is a line. It seems as if the graphs intersect near the point $\left(1,-2\right)$ .

Hence, if we zoom in on the area around this point as illustrated below, we see that although the graphs almost touch, but they do not actually intersect.