Chapter 5.1, Problem 74E

To determine

Tograph:The given functions in the same graph.

To tabulate data for the corresponding values along x-axis as given in the table.

To make a conjecture about $y_1$ and $y_2$ .

Explanation of Solution

Given information:

The given functions:

  $\begin{array}{l}{y}_1={\sec }^{4}x-{\sec }^{2}x\\ y_2={\tan }^{2}x+{\tan }^{4}x\end{array}$

The given table:

  

Graph:

Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expressions $y_1={\sec }^{4}x-{\sec }^{2}x$ and $y_2={\tan }^{2}x+{\tan }^{4}x$ , which is required to graph.

Step 4: Press GRAPH button to graph the function.

  

The curve of ${\text{Y}}_1$ is indicated by yellow line and the curve of ${\text{Y}}_2$ is indicated by black line. Both the curves coincide.

The table shows the points corresponding to $x=0.2,0.4,0.6,0.8,1.0,1.2,1.4$ values for both $y_1$ and $y_2$ .

  

Therefore, the completed table:

  

Interpretation: From the graph, it can be observed that $y_1=y_2$ .