# Thread: x and y intercepts

1. ## x and y intercepts

1) Given: F(x) =
a. Find the x-intercept(s).
b. Find the y-intercept(s).
c. Find the vertical asymptote(s) (write as an equation of a line).
d. Find the horizontal asymptote(s) (write as an equation of a line).
e. For x>4, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.
f. Find the maximum or minimum function value in the interval -4 x 4, and state whether it is a maximum or minimum value for that interval.
g. Describe what happens on the graph when x approaches infinity.

12.Given: F(x) =
a. Find the x-intercept(s).
b. Find the y-intercept(s).
c. Find the vertical asymptote(s) (write as an equation of a line).
d. Find the horizontal asymptote(s) (write as an equation of a line).
e. For x<-3, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.
f. Is the function increasing or decreasing in the interval -3 x 3?
g. As x approaches 3 from the left, what happens to the function values?
h. As x approaches 3 from the right, what happens to the function values?

I am stumped big time. Help if you can. Thanks in advance.

Kasey

2. Originally Posted by flippin4u
1) Given: F(x) =
a. Find the x-intercept(s).
b. Find the y-intercept(s).
c. Find the vertical asymptote(s) (write as an equation of a line).
d. Find the horizontal asymptote(s) (write as an equation of a line).
e. For x>4, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.
f. Find the maximum or minimum function value in the interval -4 x 4, and state whether it is a maximum or minimum value for that interval.
g. Describe what happens on the graph when x approaches infinity.
$\displaystyle f(x) = \frac{4x^2 - 1}{x^2 - 16} = \frac{(2x + 1)(2x - 1)}{(x + 4)(x - 4)}$

a) x intercepts at f(x) = 0:
So
$\displaystyle f(x) = \frac{4x^2 - 1}{x^2 - 16} = \frac{(2x + 1)(2x - 1)}{(x + 4)(x - 4)} = 0$

Implies $\displaystyle 2x + 1 = 0$ or $\displaystyle 2x - 1 = 0$

b)y intercept at x = 0. So what's f(0)?

c) Vertical asymptotes are where the denominator is 0.

d) Horizontal asymptotes are of the form y = c and x is very large. What is the function value when x is very large and when x is very large and negative? (Feel free to use a calculator if you can't see it without one.)