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12345 [234]
2 years ago
12

Match the features of the graph of the rational function.

Mathematics
1 answer:
Sunny_sXe [5.5K]2 years ago
5 0

After applying <em>algebraic</em> analysis we find the <em>right</em> choices for each case, all of which cannot be presented herein due to <em>length</em> restrictions. Please read explanation below.

<h3>How to analyze rational functions</h3>

In this problem we have a rational function, whose features can be inferred by algebraic handling:

Holes - x-values that do not belong to the domain of the <em>rational</em> function:

x³ + 8 · x² - 9 · x = 0

x · (x² + 8 · x - 9) = 0

x · (x + 9) · (x - 1) = 0

x = 0 ∨ x = - 9 ∨ x = 1

But one root is an evitable discontinuity as:

y = (9 · x² + 81 · x)/(x³ + 8 · x² - 9 · x)

y = (9 · x + 81)/(x² + 8 · x - 9)

Thus, there are only two holes. (x = - 9 ∨ x = 1) Besides, there is no hole where the y-intercept should be.

Vertical asymptotes - There is a <em>vertical</em> asymptote where a hole exists. Hence, the function has two vertical asymptotes.

Horizontal asymptotes - <em>Horizontal</em> asymptote exists and represents the <em>end</em> behavior of the function if and only if the grade of the numerator is not greater than the grade of the denominator. If possible, this assymptote is found by this limit:

y = \lim_{x \to \pm \infty} \frac {9\cdot x + 81}{x^{2}+8\cdot x - 9}

y = 0

The function has a horizontal asymptote.

x-Intercept - There is an x-intercept for all x-value such that numerator is equal to zero:

9 · x + 81 = 0

x = - 9

There is a x-intercept.

Lastly, we have the following conclusions:

  1. How many holes? 2
  2. One <em>horizontal</em> asymptote along the line where y always equals what number: 0
  3. This function has x-intercepts? True
  4. One <em>vertical</em> asymptote along the line where x always equals what number: 1
  5. There is a hole where the y-intercept should be? False

To learn more on rational functions: brainly.com/question/27914791

#SPJ1

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3 years ago
Marisa wants to buy a quality phone for least $200.She has already saved $125 and plans to save an additional $10 each week.Writ
eduard

Answer:

The inequality can be represented as:

10w+125\geq200

where w represents the number of weeks in which Maria will be able to buy a phone  for least $200.

On solving it we get : w\geq 7.5

Step-by-step explanation:

Given:

Maria wants to buy a phone for at least $200.

She has savings of $125.

She plans to save $10 every week.

To write an inequality for the situation.

Solution:

Let the number of weeks in which Maria will be able to buy a phone be = w

If she saves $10 each week.

Then, in w weeks she will save in dollars = 10w

She already has savings = $125

So her total savings in w weeks in dollars will be = 10w+125

She wants to buy a phone for at least $200.

Thus, the inequality can be represented as:

10w+125\geq200

Solving for w

Subtracting both sides by 125.

10w+125-125\geq 200-125

10w\geq 75

Dividing both sides by 10.

\frac{10w}{10}\geq \frac{75}{10}

w\geq 7.5

Thus Maria needs at least 7.5 weeks to be able to buy a phone for atleast $200.

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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