Chapter 4.6, Problem 90E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Slant Asymptote In Exercises 85-90, use a graphing utility to graph the function and determine the slant asymptote of the graph analytically. Zoom out repeatedly and describe how the graph on the display appears to change. Why does this occur? f ( x ) = x 3 − 2 x 2 + 2 2 x 2

To determine

To graph: The provided function f(x)=x32x2+22x2 and to calculate the slant asymptote.

Explanation

Given:

The function f(x)=âˆ’x3âˆ’2x2+22x2.

Graph:

The graph can be obtained using the Ti-83 calculator. Proceed as follows:

Step 1: Press the [Y=] key.

Step 2: To the right of Y1, enter the provided function.

Step 3: Press [WINDOW]. Now enter âˆ’20 for Xmin, 20 for Xmax, âˆ’20 for Ymin, 20 for Ymax.

Step 4: Press [GRAPH]

This gives:

Interpretation:

The graph shows that the as one zooms out, the graph approaches the line y=âˆ’x2+1.

First simplify the function as:

f(x)=âˆ’x3âˆ’2x2+22x2=âˆ’x3+2x2âˆ’22x2

Now compute the slant asymptote by performing long division

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