Question

Which statement describes the end behavior of the function ?Help ASAP PLEASE

Answer 1

Answer:

D  Let me know if you didn't understand anything I explained.  

Step-by-step explanation:

This is a rational function.  If you do not see why let me know and I can explain.

End behavior of a rational function has three simple rules.  You need to check the degree of the numerator and denominator though, the degree being the highest power on a variable.  so the degree of the numerator ad denominator are both 2

Now, once you know the degrees here are the rules.

if the denominator' degree is bigger than the numerator's then the end behavior is simply y = 0.  That is as the function heads toward infinity (or negative inifintiy, both are ends) the function gets closer and closer to 0

If the numerator is larger look at the leading coefficient.  if the leading coefficient is positive end behavior is infinity.  Negative is negative infinity.

If ther are both the same then take the numerator's leading coefficient and divide it by the denominator's.  So here, both have a degree of 2.  so the numerator is x^2 - 4.  x^2 is the leading term so the leading coefficient is 1.  same with the denominator.  So 1/1 = 1.  This means the end behavior is 1 just like in the fist cas the end behavior was 0.

This is basically finding the horizontal asymptotes, or when the numerator has a higher degree they are not horizontal and are called oblique asymptotes.