# How do you find the vertical, horizontal and slant asymptotes of: #f(x)=(2x) /( x-5)#?

vertical asymptote x = 5

horizontal asymptote y = 2

The denominator of f(x) cannot be zero as this is undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value of x then it is a vertical asymptote.

solve: x - 5 = 0 → x = 5 is the asymptote

Horizontal asymptotes occur as

divide terms on numerator/denominator by x

Slant asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (both of degree 1) Hence there are no slant asymptotes. graph{(2x)/(x-5) [-20, 20, -10, 10]}

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

To find the vertical asymptote, set the denominator equal to zero and solve for ( x ). Vertical asymptote: ( x = 5 ). There are no horizontal asymptotes. To find the slant asymptote, perform polynomial long division. ( f(x) = 2 + \frac{10}{x-5} ). The slant asymptote is the quotient, ( y = 2 ).

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 vertical, horizontal and oblique asymptotes for #f(x) = (3x^2 - 3x- 36) / (2x^2 + 9x +4) #?
- How do you find the end behavior of # [(x–1)(x+2)(x+5)] / [x(x+2)2]#?
- How do you find the slant asymptote of # a(x)=(2x^2-1) / (3x^3-2x+1)#?
- If #f(x) = x^2 + 3x# and #g(x) = 4x - 1#, what is #(g@f)(x)#?
- How do you find the inverse of #y = (x+3)/(x-2)# and is it a function?

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