# How do you find all the asymptotes for # (3x )/ (x+4) #?

vertical asymptote x = -4

horizontal asymptote y = 3

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation , let the denominator equal zero.

solve : x + 4 = 0 → x = -4 is the asymptote

divide terms on numerator/denominator by x

Here is the graph of the function. graph{(3x)/(x+4) [-20, 20, -10, 10]}

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

To find the asymptotes of the rational function ( \frac{3x}{x + 4} ), we need to identify any vertical, horizontal, and slant asymptotes.

Vertical Asymptote: The vertical asymptote occurs when the denominator of the rational function is equal to zero, but the numerator is not. In this case, the vertical asymptote is at ( x = -4 ) because when ( x = -4 ), the denominator becomes zero.

Horizontal Asymptote: To find the horizontal asymptote, we examine the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ). If the degrees are equal, the horizontal asymptote is at the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. In this case, the degree of the numerator (1) is less than the degree of the denominator (1), so the horizontal asymptote is at ( y = 0 ).

Slant Asymptote: A slant asymptote exists when the degree of the numerator is exactly one greater than the degree of the denominator. To find it, perform polynomial long division. Since the degrees of the numerator and denominator are equal, there is no slant asymptote for this function.

In summary, the asymptotes for ( \frac{3x}{x + 4} ) are:

- Vertical asymptote: ( x = -4 )
- Horizontal asymptote: ( y = 0 )
- No slant asymptote.

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.

- How do you find all the asymptotes for function #g(x)=e^(x-2)#?
- How do you find the vertical, horizontal or slant asymptotes for #y = x/(x-6)#?
- How do you find vertical, horizontal and oblique asymptotes for #y=1/(2-x)#?
- What is the end behavior for #F(x)=x^3 -5x+1 #?
- What is the inverse of #h(x)=-4/x^2#?

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