Q. 26 Find the roots, discontinuous, a... [FREE SOLUTION]

Chapter 1: Q. 26 (page 149)

Find the roots, discontinuous, and horizontal and vertical asymptotes of the function in Exercises 23-24. Support your answers by explicitly computing any relevant limits.
$f (x) = \frac{(x + 1) {(x - 2)}^{2}}{(x - 2) (x + 2)}$

Short Answer

Expert verified

The roots of $f (x)$ are $x = - 1, 2 .$ $f (x)$ are discontinuous at $x = 2, - 2 .$ There are no horizontal asymptotes of $f (x) .$ The vertical asymptotes of $f (x)$ are at $x = - 2 .$

Step by step solution

Step 1. Given information

The given function is $f (x) = \frac{(x + 1) {(x - 2)}^{2}}{(x - 2) (x + 2)} .$ We need to determine the roots, discontinuous, horizontal and vertical asymptotes of $f (x) .$

Step 2. Solution

$f (x) = \frac{(x + 1) {(x - 2)}^{2}}{(x - 2) (x + 2)} .$

Set $f (x) = 0 .$

$\frac{(x + 1) {(x - 2)}^{2}}{(x - 2) (x + 2)} = 0 .$

role="math" localid="1648223264513" $(x + 1) (x - 2) = 0 .$

$x = - 1, 2 .$

The roots of the function are $x = - 1, 2 .$ The function $f (x)$ are discontinuous at $x = 2, - 2 .$ There are no horizontal asymptotes of $f (x) .$ The value of $x$ that cause the denominator asymptotes are $x = - 2 .$

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91影视

Find the roots, discontinuous, and horizontal and vertical asymptotes of the function in Exercises 23-24. Support your answers by explicitly computing any relevant limits.
$f (x) = \frac{(x + 1) {(x - 2)}^{2}}{(x - 2) (x + 2)}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solution

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91影视

Find the roots, discontinuous, and horizontal and vertical asymptotes of the function in Exercises 23-24. Support your answers by explicitly computing any relevant limits. fx=x+1x-22x-2x+2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Discrete Mathematics

Statistics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the roots, discontinuous, and horizontal and vertical asymptotes of the function in Exercises 23-24. Support your answers by explicitly computing any relevant limits.
$f (x) = \frac{(x + 1) {(x - 2)}^{2}}{(x - 2) (x + 2)}$