Question

Given the function f(x)= x2-81/x2-11x+18 on your graphing calculator, what is the most appropriate viewing window to see the graph?
a Xmin: –10, Xmax: 10
Ymin: –10, Ymax: 10

b Xmin: –5, Xmax: 5
Ymin: –5, Ymax: 5

c Xmin: 0, Xmax: 10
Ymin: 0, Ymax: 10

d Xmin: –10, Xmax: 0
Ymin: –10, Ymax: 0

i figured it out, its a

Answer 1

Answer:

The correct option is a.

Step-by-step explanation:

The given function is

$f\left(x\right)=\frac{\left x^2-81\right}{x^2-11x+18}$

It can be written as

$f\left(x\right)=\frac{\left(x-9)(x+9)}{(x-9)(x-2)}$

$f\left(x\right)=\frac{\left x+9}{x-2}$

Put x=0 to find y-intercept.

$f(0)=\frac{0+9}{0-2}=-4.5$

The y-intercept is (0,-4.5).

Put f(x)=0 to find x-intercept.

$0=\frac{x+9}{x-2}\Rightarrow x=-9$

The x-intercept is (-9,0).

Equate denominator equal to 0, to find the vertical asymptote.

$x-2=0\Rightarrow x=2$

The vertical asymptote is x=2.

Take limit x tends to infinity, to find horizontal asymptote.

$lim_{x\rightarrow \infty}f(x)=lim_{x\rightarrow \infty}\frac{x+9}{x-2}$

$lim_{x\rightarrow \infty}f(x)=lim_{x\rightarrow \infty}\frac{x(1+\frac{9}{x})}{x(1-\frac{2}{x})}$

Apply limits,

$lim_{x\rightarrow \infty}f(x)=1$

The horizontal asymptote is y=1.

Since the intercepts and asymtotes lie in the window, i.e., Xmin: –10, Xmax: 10

, Ymin: –10, Ymax: 10, thus the correct answer would be option a.

Answer 2

I think is A not sure