Chapter 1.4, Problem 2E

To determine

Find the most appropriate graph of the function.

Answer to Problem 2E

  $\left(d.\right)$$\boxed{\left[-5,5\right]by\left[-50,50\right]}$

Explanation of Solution

Given information:

Use a graphic calculator or computer to determine which of the given viewing rectangle produces the most appropriate graph of the function $f\left(x\right)=x^4-16x^2+20$ .

  $\left(a.\right)$$\left[-3,3\right]$ By $\left[-3,3\right]$

  $\left(b.\right)$$\left[-10,10\right]$ By $\left[-10,10\right]$

  $\left(c.\right)$$\left[-50,50\right]$ By $\left[-50,50\right]$

  $\left(d.\right)$$\left[-5,5\right]$ By $\left[-50,50\right]$

Calculation:

Here, we will consider the function $f\left(x\right)=x^4-16x^2+20$ .

We have to determine which of the viewing rectangles produces the most appropriate graph of the given function.

Now, viewing rectangle $\left(a.\right)$$\left[-3,3\right]$ by $\left[-3,3\right]$ :

We will first graph the function on the viewing rectangle $\left[-3,3\right]$ by $\left[-3,3\right]$ .

Here, we will use $TI-83$ calculator.

Now, press on $\boxed{WINDOW}$ button and set the scale as shown below:

  

Press on $\boxed{Y=}$ button and enter the given equation:

  

Press on $\boxed{GRAPH}$ button to get the graph of the given function:

  

The graph of the function is not visible on this viewing rectangle $\left[-3,3\right]$ by $\left[-3,3\right]$ .

Now, viewing the rectangle $\left(b.\right)$$\left[-10,10\right]$ by $\left[-10,10\right]$ :

We will graph the function on the viewing rectangle $\left[-10,10\right]$ by $\left[-10,10\right]$ .

Press on $\boxed{WINDOW}$ button and set the scale as shown below:

  

Press on $\boxed{Y=}$ button and enter the given equation.

  

Press on $\boxed{GRAPH}$ button to get the graph of the given function:

  

Now, viewing the rectangle $\left(c.\right)$$\left[-50,50\right]$ by $\left[-50,50\right]$

We will graph the function on the viewing rectangle $\left[-50,50\right]$ by $\left[-50,50\right]$ .

Press on $\boxed{WINDOW}$ button and set the scale as shown below:

  

Press on $\boxed{Y=}$ button and enter the given equation.

  

Press on $\boxed{GRAPH}$ button to get the graph of the given function:

  

Now, viewing the rectangle $\left(d.\right)$$\left[-5,5\right]$ by $\left[-50,50\right]$

We will graph the function on the viewing rectangle $\left[-5,5\right]$ by $\left[-50,50\right]$ .

Press on $\boxed{WINDOW}$ button and set the scale as shown below:

  

Press on $\boxed{Y=}$ button and enter the given equation.

  

Press on $\boxed{GRAPH}$ button to get the graph of the given function:

  

Now, the graph of the function is visible clearly on this viewing rectangle $\left[-5,5\right]$ by $\left[-50,50\right]$ .

Hence, by observing the above four graphs we can conclude that the viewing rectangle $\left[-5,5\right]$ by $\left[-50,50\right]$ produces the most appropriate graph of the function $f\left(x\right)=x^4-16x^2+20$ and thus $\left(d.\right)$$\left[-5,5\right]$ by $\left[-50,50\right]$ , is correct viewing rectangle.