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

kjukks1234531 2022-09-18 Answered
How do you graph f ( x ) = 3 x + 8 x - 2 using holes, vertical and horizontal asymptotes, x and y intercepts?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Jamari Morgan
Answered 2022-09-19 Author has 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]}

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-25
True or False. The graph of a rational function may intersect a horizontal asymptote.
asked 2022-09-02
If y varies inversely as x, and y = 3 when x = 6, how do you find the value of x when y = 18?
asked 2022-09-10
How do you simplify 8 x 5 - 10 x y 2 2 x y 2 and what are the excluded values of the variables?
asked 2022-02-16
In Hartshorne's Algebraic Geometry the function field K(Y) of a variety Y is defined as the set of equivalence classes with f being a regular function on the open subset U. We have = if f and g agree on UV.
How does one evaluate a "rational function on Y'' f? Is it f(P) using the Evaluation map for polynomials? In this case, I don't see that this is well defined: Let PUV and =, then g(P) might not even be defined!
asked 2022-07-16
could any one give me a hint for this one? please not the whole solution Let f be a non constant rational function and z 1 , , z n be its poles in C ¯ . we have to show that f can be written as f = f 1 + , f p where each f j is a rational function.
asked 2022-09-05
If y varies inversely as x, how do you find the constant of variation if y=36 when x=9?
asked 2022-06-27
I have the function: f ( x ) = 2 x 2 x + 2
I know that this function has an oblique asymptote, but all the tutorials I can find on google, are with rational functions with the form:
f ( x ) = P ( x ) Q ( x )
Where they simply just divide the denominator with the numerator.
But I can't do that, because my equation doesn't contain any fractions. So my question is: how do I find the function to the oblique asymptote for my f ( x )?