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Sav [38]
3 years ago
13

Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.

Mathematics
1 answer:
gladu [14]3 years ago
5 0

Answer:

Vertical asymptote: x=3

Horizontal asymptote: f(x) =2

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

f (x) = -\dfrac{1 }{ x-3} +2

One root, x = 3.5

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

<em>Roots of f(x) means the value of x where f(x) = 0</em>

0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5

One root, x = 3.5

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) \rightarrow \infty

For all, other values of x , f(x) is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is \frac{1}{x-3}.

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) \rightarrow \infty.

-\dfrac{1 }{ x-3} +2 \rightarrow \infty

It is possible only when

x-3=0\\\Rightarrow x=3

\therefore vertical asymptote: x=3

Horizontal Asymptote is the value of f(x) , where value of x \rightarrow \infty.

x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2

\therefore Horizontal asymptote: f(x) =2

Please refer to the graph of given function as shown in the attached image.

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Answer:

Step-by-step explanation:

Hello!

The variable of interest is

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If the claim is μ ≠ 12, its complement is μ = 12, the expression carrying the "=" sign will be the null hypothesis and its complement will be the alternative hypothesis:

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The decision rule is:

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If -2.069 < t_{H_0} < 2.069, then you do not reject the null hypothesis.

The value is less than the left critical value, the decision is to reject the null hypothesis.

Then you can say that with a 5% significance level, there is significant evidence to reject the null hypothesis, then the average amount of root beer of the Windsor Bottling Company is different from 12 oz, this means that the claim about the amount of root beer in the cans is correct.

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