Question

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.

Answer 1

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

d is correct

Answer 2

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.

`f(x)=(k)/((x-2)(x+2))\\\\ f(x)=(k)/(x^2-4)\\\\ Now,\lim_(x \to \infty) (k)/(x^2-4)= (k)/((\infty)^2-4)\\\\\lim_(x \to \infty) f(x)=(k)/(\infty)=0`

,2.

`\lim_(x \to -\infty) f(x)= \lim_(x \to -\infty)(k)/(x^2-4)\\\\=(k)/((-\infty)^2-4) \\\\ =(k)/(\infty) \\\\=0`

3.

`\lim_(x \to 0) f(x)= \lim_(x \to 0)(k)/(x^2-4)\\\\=(k)/((0)^2-4) \\\\ =(k)/(-4)`

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