Sketch the graph of each rational function showing all the key features. verify your graph by graphing the function on
the graphing calculator.
10. f(x) = x3 − 8 / x − 1

The graph crosses the x axis at x=0. For x> 0, it rises to a maximum value and then decreases toward y= 0 as x goes to infinity. For x< 0, it decreases to a minimum values then rises toward y= 0 as x goes to negative infinity. y= 0 is a horizontal asymptote but the graph crosses y= 0 at x= 0.

Step-by-step explanation:

A common mistake that students make is to think that a graph cannot cross a slant or horizontal asymptote. This is not the case! A graph CAN cross slant and horizontal asymptotes (sometimes more than once). It's those vertical asymptote critters that a graph cannot cross.

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are