How do you graph f(x)=(x^2−1)/x using holes, vertical and horizontal asymptotes, x and y intercepts?

tonan6e 2022-09-30 Answered
How do you graph f ( x ) = x 2 - 1 x 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)

Maddox Koch
Answered 2022-10-01 Author has 7 answers
You know this graph can't exist at x=0, since that would make the denominator equal 0. Because the polynomial on the top is of a bigger degree, there is a slant asymptote. Dividing the initial terms, we get x 2 x = x , so there is a slant asymptote at y=x.
Since we can factor the top into (x−1)(x+1), we know the function has two solutions at x = ± 1 .

Plotting these solutions and following the asymptotes makes this a straightforward graph to sketch: graph{(x^2-1)/x [-10, 10, -5, 5]}

Also, not all rational functions are so easy to pblackict the behavior of, so creating a table of x and y values is always a good idea! And if you need more information about how to find the asymptotes, look here.
Did you like this example?
Subscribe for all access

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 operate could encounter a horizontal straight line.

asked 2022-06-20
For a field k, let V be an affine variety over k. Denote by k ( V ) the function field of V, containing all rational functions r : V A k 1 . My question is, if a rational function f k ( V ) has a pole at p V, is there an expression f = g h where g , h k [ V ] are regular functions, and g ( p ) 0, h ( p ) = 0?
When V A k 1 , this is clear, since if we have f = g h where g ( p ) = h ( p ) = 0, we can simply reduce the expression of g and h and eliminate the factor ( x p ) until we get f = g h such that g ( p ) 0, h ( p ) = 0. But when g , h are multivariate functions, I wonder how to get such a reduced expression?
asked 2021-09-11
Determine
limxf(x)
and
limxf(x)
for the following rational functions. Then give the horizontal asymptote of f (if any).
f(x)=4x278x2+5x+2
asked 2022-09-02
If f(x) varies directly with x and f(x) = 24 when x = –4, then what is f(x) when x = 12?
asked 2022-06-24
I want to decompose the rational function
P ( s ) Q ( s ) = i = 1 m ( s + a i ) i = 1 n ( s + b i )
where a i > 0 for every i = 1 , , m b i > 0 for every i = 1 , , n and n > m.
In other words, I'm looking for coefficients x j , j = 1 , n such that
P ( s ) Q ( s ) = x 1 s + b 1 + + x n s + b n j = 1 n x j i = 1 i j n ( s + b i ) = i = 1 m ( s + a i )
Making some attempts with Mathematica for low values of m and n it seems that the x j are given by
x j = i = 1 m ( a i b j ) i = 1 i j n ( b i b j )
So my questions are:
1) Can I say beforehand that there exist unique such x j s?
2) How can I prove that x j has in general (as it seems) the form above?
asked 2022-02-18
After having read abstract concepts of algebraic curves, I have trouble dealing with actual examples. For instance, why is the ϕ=yx a rational function on the curve F=y2+y+x2? I know that any rational function on this curve should be of the form {ϕ=fg:f,gK[x,y](F),g0}, but what do I need to actually check to show that this is a rational function on F? Any help will be good
asked 2022-09-02
If y varies inversely as the cube of x and directly as the square of z and y = -6 when x=3 and z =9, how do you find y when x =6 and z= -4?