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f(x)=-2x^2+14/x^2-49 which statement describes the behavior of the graph of the function shown at the vertical asymptotes?

fx2x214x249 which statement describes the behavior of the graph of the function shown at the vertical asymptotes class=

Respuesta :

touheed050

Answer:

Option 3 :

x → 7+, y → –[infinity]

Step-by-step explanation:

f(x) = (-2x² + 14)/(x² - 49)

x² - 49 = (x + 7)(x - 7)

Hence f(x) goes to infinity at x = - 7 or 7

x < - 7 = (-ve)(-ve) = + ve

=> x → –7–

Here, x² - 49 is + ve

-7 < x < 7 = (+ve)(-ve) = - ve

=> x → –7+ or x → 7– .

here, x² - 49 is - ve

x > 7 = (+ve)(+ve) = + ve

=> x → 7+

Here, x² - 49 is + ve

So (-2x² + 14) is - ve for all [ x → –7– , x → –7+ , x → 7– , x → 7+ ]

As,

-2(-7)² + 14 = -84 and -2(+7)² + 14 = -84

x → –7– = (-ve)/(+ve)

=> y → -[infinity].

x → –7+ or x → 7– = (-ve)/(-ve)

=> y → [infinity]

x → 7+ = (-ve)/(+ve)

=> y → -[infinity].

x → 7+, y → –[infinity]. is the correct option

The statement (C) as x approaches 7 from the left, y approaches -∞ describe the behavior of the graph of the function.

What is a function?

It is defined as a spceial type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a rational function:

[tex]\rm f(x) =\dfrac{-2x^2+14}{x^2-49}[/tex]

x² - 49 cannot be zero:

x² - 49 ≠ 0

x ≠ 7, x ≠  -7

From the graph, as x approaches 7 from the left, y approaches -∞

Thus, the statement (C) as x approaches 7 from the left, y approaches -∞ describe the behavior of the graph of the function.

Learn more about the function here:

brainly.com/question/5245372

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