oliviawhite1015
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Which statement is true about the end behavior of the graphed function?
a.As the x-values go to positive infinity, the function's values go to negative infinity.
b.As the x-values go to zero, the function's values go to positive infinity.
c.As the x-values go to negative infinity, the function's values are equal to zero
d.As the x-values go to positive infinity, the function's values go to positive infinity.

Which statement is true about the end behavior of the graphed function aAs the xvalues go to positive infinity the functions values go to negative infinity bAs class=

Respuesta :

Look at the positive side of x axis  
as x approaches infinity  so does the value of the function

d is correct

Answer with explanation:

The given curve has two vertical Asymptote,

First, x=2

And,Second , x= -2

So,the equation of the curve can be written as

1.

 [tex]f(x)=\frac{k}{(x-2)(x+2)}\\\\ f(x)=\frac{k}{x^2-4}\\\\ Now,\lim_{x \to \infty} \frac{k}{x^2-4}= \frac{k}{(\infty)^2-4}\\\\\lim_{x \to \infty} f(x)=\frac{k}{\infty}=0[/tex]

,2.

[tex]\lim_{x \to -\infty} f(x)= \lim_{x \to -\infty}\frac{k}{x^2-4}\\\\=\frac{k}{(-\infty)^2-4} \\\\ =\frac{k}{\infty} \\\\=0[/tex]

3.

[tex]\lim_{x \to 0} f(x)= \lim_{x \to 0}\frac{k}{x^2-4}\\\\=\frac{k}{(0)^2-4} \\\\ =\frac{k}{-4}[/tex]

Option C: As the x-values go to negative infinity, the function's values are equal to zero