Graph the functions yx - 2%3!

Name: Graph the functions yx - 2%3!
Uploaded: 2024-03-20T06:47:22.000Z
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Description: Graph the functions yx - 2%3!

Consider the given: y=1x-2Let y=fxfx=1x-2 To graph the function, calculate: Domain of 1x-2:…

Answered: y x - 2 %3!

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter6: Fractions

Section6.1: Simplifying Fractions

Problem 32WE

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Graph the functions

Expert Solution

Step 1

Consider the given:

$\begin{array}{l} y = \frac{1}{x - 2} \\ Let y = f (x) \\ f (x) = \frac{1}{x - 2} \end{array}$

To graph the function, calculate:

$\begin{array}{l} Domain of \frac{1}{x - 2} : (- \infty, 2) \cup (2, \infty) \\ Range of \frac{1}{x - 2} : (- \infty, 0) \cup (0, \infty) \end{array}$

Step 2

Step 3

Find the vertical asymptotes.

Vertical asymptotes will be generated by the zeros of the denominator.

Set the denominator equal to zero and solve.

Find the horizontal asymptotes.

Horizontal asymptotes can be calculated as-

If denominator's degree > numerator's degree, the horizontal asymptote is the x-axis, y=0.

If denominator's degree < numerator's degree, then there is no horizontal asymptotes.

If the degrees are equal, the asymptote will be y equals to ratio of numerator's leading coefficient and denominator's leading coefficient.

$\begin{matrix} y = \frac{1}{x - 2} \\ Numerator' s Degree = 0 \\ Denominator' s Degree = 1 \\ H e r e, \\ Denominator' s degree > Numerator' s degree \\ y = 0 \\ Horizontal asymptote, y = 0 \end{matrix}$

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