# How do you find all the asymptotes for function #f(x) = (x+3)/(x-3)#?

I found the two asymptotes:

1] Vertical:

2] Horizontal:

Have a look:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the asymptotes of the function f(x) = (x + 3)/(x - 3), we need to identify the vertical asymptotes and the horizontal asymptote.

Vertical asymptotes occur where the denominator of the function becomes zero but the numerator does not. In this case, the denominator x - 3 becomes zero when x = 3. Therefore, there is a vertical asymptote at x = 3.

Horizontal asymptotes occur when the degree of the numerator and the degree of the denominator are the same. In this function, both the numerator and denominator are polynomials of degree 1. Therefore, to find the horizontal asymptote, we compare the leading coefficients of the numerator and the denominator. The leading coefficient of the numerator is 1, and the leading coefficient of the denominator is also 1. Since the degrees are the same and the leading coefficients are equal, the horizontal asymptote is the ratio of the leading coefficients, which is 1/1 = 1.

So, the vertical asymptote is x = 3, and the horizontal asymptote is y = 1.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Given #h(x)=e^-x#, how do you describe the transformation?
- How do you find the asymptote and holes for #y=(x-6)/(x^2+5x+6)#?
- How do you find the asymptotes for #f(x)= (4x^2+5)/( x^2-1)#?
- How do you find vertical, horizontal and oblique asymptotes for #f(x)= (x^2-5x+6)/ (x^2-8x+15)#?
- How do you find the asymptotes for #(x-4)/(x^2-3x-4)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7