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ladessa [460]
3 years ago
14

Given the function f(x)= x2-81/x2-11x+18 on your graphing calculator, what is the most appropriate viewing window to see the gra

ph?
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

Mathematics
2 answers:
Roman55 [17]3 years ago
6 0

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.

Vika [28.1K]3 years ago
4 0
I think is A not sure
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