Question

find the x and y intercept, find the vertical asymptote
1. f(x) = x/2
2. f(x) = x+1/4​

Answer 1

Answer:

here is your answer :-

Step-by-step explanation:

Given What are the vertical and horizontal asymptotes for the function f (x) =   3x^2 / x^2 – 4  

We need to find the function f(x) = 3x^2 / x^2 – 4

Now the given equation is undefined for x = 2, - 2

When x tends to 2 the expression 3x^2 / x^2 – 4 tends to infinity from the left as well as from the right, so x = 2 is a vertical asymptote.

When x tends to - 2 the expression 3x^2 / x^2 – 4 tends to infinity from the left as well as from the right, so x = - 2 is a vertical asymptote.

Hence the vertical asymptotes are x = - 2, 2

Let the rational function R (x) = p x^n / q x^m where n and m are degree of numerator and denominator.

If n < m, then the y axis y = 0 is a horizontal asymptote.

If n = m then horizontal asymptote is the line y = p/q

We need to find n and m when n = 2 and m = 2

Since n = m the horizontal asymptote is the line y = p/q where p = 3 and q = 1

Therefore y = 3

Now the vertical asymptotes x = - 2, 2

Horizontal asymptotes y = 3