Question

What are the asymptotes of the function?
f(x)=x^2-7x-8/
2x^2-8
Drag the equations into the boxes to correctly complete the table.
x=18
H=
12
Vertical asymptote
x=-7
x = 2
x=12
X= 7
x = -1
heckpoint: Lessons 3-4
X=8
Horizontal asymptote
y=-8 y=-7
1
y=2
y=-2
y=7
y=-1
y = 8
2 3 4 5 6 7

8

Answer 1

In accordance with concepts of horizontal and vertical asymptotes, the rational function has a horizontal asymptote (y = 1/2) and two vertical asymptotes (x = 2, x = - 2).

How to determine the asymptotes related to a rational function

There are two kinds of asymptotes that can be found. Horizontal asymptotes are found by definition of limit and vertical asymptotes are so by finding the roots of the denominator.

Horizontal asymptote

$y = \lim_{x \to \pm \infty} \frac{x^{2}-7\cdot x - 8}{2\cdot x^{2}-8}$

$y = \lim_{x \to \pm \infty} \frac{x^{2}-7\cdot x - 8}{2\cdot x^{2}-8} \cdot \frac{x^{2}}{x^{2}}$

$y = \lim_{x \to \pm \infty} \frac{1 - \frac{7}{x}-\frac{8}{x^{2}}}{2 - \frac{8}{x^{2}} }$

$y = \frac{1}{2}$

Vertical asymptotes

2 · x² - 8 = 0

2 · x² = 8

x² = 4

x = ± 2

There are two vertical asymptotes: x = 2, x = - 2

In accordance with concepts of horizontal and vertical asymptotes, the rational function has a horizontal asymptote (y = 1/2) and two vertical asymptotes (x = 2, x = - 2).

To learn more on asymptotes: https://brainly.com/question/4084552

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