# Math - Domain and Asymptotes

Given the following rational function:
f(x) = (x^2 + 6x - 8) / (x – 5)

(a) state the domain.

(b) find the vertical and horizontal asymptotes, if any.

(c) find the oblique asymptotes, if any.

1. 👍 0
2. 👎 0
3. 👁 240
1. Given the rational function:
f(x) = (x^2 + 6x - 8) / (x – 5)

a. Domain
The domain of a rational function is all real numbers minus points where the denominator (x-5) become zero. Here the point to be removed is x-5=0, or x=5.
The answer in interval notation would be:
(-&infin,5)∪(5,∞)
which is essentially all real less x=5.

b. Asymptotes
Vertical asymptotes occur when the denominator becomes zero. There is one such asymptote for f(x).
Hint: this point has been identified in part (a) above.
Horizontal asymptotes are limits of f(x) as x→-∞ or x→∞.
If these limits do not exist, there are no horizontal asymptotes.
Hint: Evaluate Lim x→±∞ and see if the limits exist.

3. oblique asymptotes
Oblique asymptotes exist when the leading term of the numerator divided by the leading term of the denominator yields a linear term (i.e. of the form kx), where k≠0.

Here, the leading term of the numerator is x^2, and that of the denominator is x.
The quotient is therefore x^2/x=x (k=1).
The oblique asymptote is therefore y=x.
http://imageshack.us/photo/my-images/221/1307663049.png/

1. 👍 0
2. 👎 0
2. x^2+x-6/x+3

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Pre Algebra

1.Which of the following numbers is rational? A \frac{4}{5} B √27 C 4.02002000200002... D √31 2.What type of number is shown below? 0.3133113331... A repeating decimal B rational C irrational D terminating 3.Select all the

asked by Cammie on September 24, 2017
2. ### Gr.11 - Rational functions graphing.

1. Identify a rational function whose graph is a horizontal line except for two holes. Graph the function. 2. Identify a rational function who graph lies entirely above the x-axis and has a single vertical asymptote. Graph the

asked by Mae on October 6, 2008
3. ### Alegbra 2

Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with

asked by Chelsey on January 26, 2018

Create a rational function such that the graph of has vertical asymptotes at x=5 and x= -7, a hole at x=2 , and a horizontal asymptote at y = 14. By creating a rational function, you are to write rule for this function. There are

asked by Brianna on October 16, 2011
1. ### functions

Identify a rational function whose graph is a horizontal line except for two holes. Graph function.

asked by Tori on September 29, 2010
2. ### algebra

Using the rational zeros theorem to find all zeros of a polynomial The function below has at least one rational zero. Use this fact to find all zeros of the function h(x)=7x^4-9x^3-41x^2+13x+6 if more than one zero, separate with

asked by Pat on October 17, 2015
3. ### Math

Which combination could create the function f(x)= x√x? adding a rational function and a linear function adding a linear function and a logarithmic function multiplying a linear function and a square-root function dividing an

asked by tobeymaguire on June 19, 2020
4. ### algebra

the rational function has a y-intercept of 7. what is the equation for this function

asked by helana on November 9, 2018
1. ### Algebra

For the polynomial function, (a) list all possible rational zeros, (b) find all rational zero, and (c) factor f(x)! f(x)=6x^3+13x^2_41x+12

asked by Georgette on December 4, 2015
2. ### Math

Write a rational function satisfying the following criteria. vertical Asymptote: x=-1, slant asymptote: y=x+2, zero of the function: x=3 I had f(x)=x^2+3x+2/x+1, that only works for the asymptotes and not the zero can someone

asked by Anonymous on January 19, 2015
3. ### Math

Which set of numbers best describes the displayed weights on a digital scale that shows each weight to the nearest half of pound. A) Whole B) Rational C) Real D) Integers My answer is Rational because rational numbers can be

asked by Tamara on September 7, 2015
4. ### Math

Jeremy is playing a game called “Rational Round Up” where he has to collect all the numbers in a maze that are rational and then get to the end of the maze. When he collects a number, he must prove it is rational by writing it

asked by Jake on December 12, 2019