Graph y = x^3 and y = 16/x on the same set of coordinate axes. Use the graphs to find the exact solutions to the equation x^3 = 16/x

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#1

Graph y = x^3 and y = 16/x on the same set of coordinate axes. Use the graphs to find the exact solutions to the equation x^3 = 16/x . Verify by substitution that they satisfy the equation.

Answer:

Use your graphing calculator to enter the different graphs. Select Y= , it should be one of the top-left buttons on your calculator. Enter each function separately. The first one is x^3 and the second is 16/x. If you do not have a graphing calculator, use a site like in order to draw the graphs.

Once drawn, find the points using the CALC button and then select INTERSECT, then move the ‘x’ around with your arrow buttons, and answer the questions that are located at the bottom of the screen, then select enter. Make sure your window is set to -10 minimum and 10 maximum on both the x and y values.

After doing this, you should find the following points of intersection:

(2,8),(-2,-8)

To test these points, plug in the x value into each equation and verify that the y-value equals either 8 or -8.

First Equation:
y=(2)^3=8
y=(-2)^3=-8

Second Equation:
y=16/(2)=8
y=16/(-2)=-8

Both points are valid