How do you graph f(x)=(3x+8)/(x−2) using holes, vertical and horizontal asymptotes, x and y intercepts?

kjukks1234531

kjukks1234531

Answered question

2022-09-18

How do you graph f ( x ) = 3 x + 8 x - 2 using holes, vertical and horizontal asymptotes, x and y intercepts?

Answer & Explanation

Jamari Morgan

Jamari Morgan

Beginner2022-09-19Added 10 answers

Asymptotes
The denominator of f(x) cannot be zero as this would make f(x) 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 then it is a vertical asymptote.
solve : x - 2 = 0 x = 2 is the asymptote
Horizontal asymptotes occur as
lim x ± , f ( x ) c ( a constant)
divide terms on numerator/denominator by x
f ( x ) = 3 x x + 8 x x x - 2 x = 3 + 8 x 1 - 2 x
as x ± , f ( x ) 3 + 0 1 - 0
y = 3 is the asymptote
Holes occur when there is a duplicate factor on the numerator/denominator. This is not the case here, hence there are no holes.
Intercepts
x = 0 f ( 0 ) = 8 - 2 = - 4 y-intercept
y = 0 3 x + 8 = 0 x = - 8 3 x-intercept
graph{(3x+8)/(x-2) [-20, 20, -10, 10]}

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