Please help with a step by step solution to this problem x²-2xFind all pertinent information and sketch the graph of f(x) =x²-4Find all asymptotes:HA:VA:Find the coordinates of:x-intercept:y-intercept:hole:Sketch the graph.

Answered: x²-2x Find all pertinent information…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Please help with a step by step solution to this problem

x²-2x
Find all pertinent information and sketch the graph of f(x) =
x²-4
Find all asymptotes:
HA:
VA:
Find the coordinates of:
x-intercept:
y-intercept:
hole:
Sketch the graph.

Expert Solution

Step 1

Given:

$f (x) = \frac{x^{2} - 2 x}{x^{2} - 4}$

To find :

Horizontal asymptote, vertical asymptote , coordinates of $x$ -intercept and $y$ -intercept and hole.

Also to sketch the given function.

Horizontal asymptote is a line which approaches to some curve as $x \to \infty o r x \to - \infty$ .

Vertical asymptote is a line whose distance from a function gets decreasing and approaches zero.

$x$ -intercept is the value at which graph of the function crosses $x$ -axis.

$y$ -intercept is the value at which graph of the function crosses $y$ -axis.

Removable discontinuity is defined as the point at which limit of the function exists but does not equal to the value of the function at that point.

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x²-2x Find all pertinent information and sketch the graph of f(x) = x²-4 Find all asymptotes: HA: VA: Find the coordinates of: x-intercept: y-intercept: hole: Sketch the graph.