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valentinak56 [21]
1 year ago
10

Show all work to identify the asymptotes and state the end behavior of the function f(x)=5x/x-25

Mathematics
1 answer:
Nina [5.8K]1 year ago
6 0

Using the asymptote concept, it is found that:

  • The vertical asymptote is of x = 25.
  • The horizontal asymptote is of y = 5.
  • Considering the horizontal asymptote, it is found that the end behavior of the function is that it tends to y = 5 to the left and to the right of the graph.

<h3>What are the asymptotes of a function f(x)?</h3>

  • The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
  • The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, the function is:

f(x) = \frac{5x}{x - 25}

Considering the denominator, the vertical asymptote is:

x - 25 = 0 -> x = 25.

The horizontal asymptote is found as follows:

y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = \lim_{x \rightarrow \infty} 5 = 5

Hence the end behavior of the function is that it tends to y = 5 to the left and to the right of the graph.

More can be learned about asymptotes and end behavior at brainly.com/question/28037814

#SPJ1

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Hi there the answer will be (3,11)

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The standard forrm equation of the circle is (x-h)² + (y-k)² = r²
where h,k : x,y-coordinate of the center
           r : radius of the circle
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                                             k = (y1 + y2)/2 = (4+2)/2 = 3
=> the center is (7,3)
Because the given information gave 2 endpoints so we can choose one of these, then use the distance formula to get the radius
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                                            r = √(9 - 7)² + (4 - 3)²
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Finally, the equation of the circle is (x - 7)² + (y - 3)² = (√5)²
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Answer:

The three expressions are the first option, the third option, and the forth option

Step-by-step explanation:

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