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ladessa [460]
2 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]2 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]2 years ago
4 0
I think is A not sure
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Answer:

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Step-by-step explanation:

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  tan (180 - x) = -tan x)

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# 360 - x ⇒ fourth quadrant (sin (180 - x) = -sin x , cos (180 - x) = cos x

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∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)

- From the rules above cos x = cos(-x)

∴ cos x cos (-x) = cos x cos x

∴ cos x cos (-x) = cos² x

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∴ sin x sin (-x) = sin x [- sin x]

∴ sin x sin (-x) = - sin² x

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2 years ago
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144 gold bars

Step-by-step explanation:

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4 0
3 years ago
What is the area of this octagon
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Answer:

59cm^2

Step-by-step explanation:

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4 0
2 years ago
Suppose that 80 percent of all statisticians are shy, whereas only 15 percent of all economists are shy. Suppose also that 90 pe
Anna71 [15]

Answer:

37.21% probability that the person is a statistician.

Step-by-step explanation:

We have these following probabilities:

An 80% probability that a statistican is shy.

A 15% probability that an economist is shy.

At the gathering, a 90% probability that a person is an economist.

At the gathering, a 10% probability that a person is a statistican.

If you meet a shy person at random at the gathering. What is the probability that the person is a statistician?

This can be formulated as the following question:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

P = \frac{P(B).P(A/B)}{P(A)}

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

So

What is the probability that the person is a statistican, given that he is shy?

P(B) is the probability of the person being a statistican. So P(B) = 0.1.

P(A/B) is the probability of a statistican being shy, so P(A/B) = 0.8.

P(A) is the probability of a person being a shy. This is 15% of 90%(economists) and 80% of 10%(statisticans). So

P(A) = 0.15*0.9 + 0.8*0.1 = 0.215

Finally

P = \frac{P(B).P(A/B)}{P(A)}

P = \frac{0.1*0.8}{0.215} = 0.3721

37.21% probability that the person is a statistician.

3 0
3 years ago
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