Chapter 14: Q. 83 (page 890)

For Problems 83 – 88, use a graphing utility to graph the functions R given in Problems 77– 82. Verify the solutions found above.
$R (x) = \frac{x^{3} - x^{2} + x - 1}{x^{4} - x^{3} + 2 x - 2}$

Short Answer

Expert verified

Using the graphing utility the asymptotes and holes of the function $R (x) = \frac{x^{3} - x^{2} + x - 1}{x^{4} - x^{3} + 2 x - 2}$ are verified.

Step by step solution

Step 1. Given Information

We are given a rational function $R (x) = \frac{x^{3} - x^{2} + x - 1}{x^{4} - x^{3} + 2 x - 2}$ .

We need to use a graphing utility and verify the asymptotes and holes of the function.

Step 2. Graph the function and verify the result

The graph of the function $R (x) = \frac{x^{3} - x^{2} + x - 1}{x^{4} - x^{3} + 2 x - 2}$ is given as

It can be seen that the graph is discontinuous at two points. At $x = - \sqrt[3]{2}$ there is a vertical asymptote and at $x = 1$ there is a hole at $(1, \frac{2}{3})$ .

So the results are verified.

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For Problems 83 – 88, use a graphing utility to graph the functions R given in Problems 77– 82. Verify the solutions found above.
$R (x) = \frac{x^{3} - x^{2} + x - 1}{x^{4} - x^{3} + 2 x - 2}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph the function and verify the result

One App. One Place for Learning.

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For Problems 83 – 88, use a graphing utility to graph the functions R given in Problems 77– 82. Verify the solutions found above.R(x)=x3-x2+x-1x4-x3+2x-2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph the function and verify the result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Statistics

Discrete Mathematics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

For Problems 83 – 88, use a graphing utility to graph the functions R given in Problems 77– 82. Verify the solutions found above.
$R (x) = \frac{x^{3} - x^{2} + x - 1}{x^{4} - x^{3} + 2 x - 2}$