How do you graph f(x)=(x^2−2x)/(x^2−4) using holes, vertical and horizontal asymptotes, x and y intercepts?

Aden Lambert

Aden Lambert

Answered question

2022-11-07

How do you graph f ( x ) = x 2 - 2 x x 2 - 4 using holes, vertical and horizontal asymptotes, x and y intercepts?

Answer & Explanation

petyelebxu

petyelebxu

Beginner2022-11-08Added 13 answers

We can factor f(x).

f ( x ) = x ( x - 2 ) ( x + 2 ) ( x - 2 )

f ( x ) = x x + 2

This means that there will be a hole at x=2. There will be a vertical asymptote at x=−2.

The horizontal asymptote will occur at the ratio between the highest power in the numerator and in the denominator (only if the powers are equal).

Hence, there will be a horizontal asymptote at y = 1 1 = 1 .

As for intercepts, the graph will pass through the origin, and the origin will serve as the x and y intercept.

Here is the graph:

graph{(x^2 - 2x)/(x^2 - 4) [-10, 10, -5, 5]}

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