Graph Rational Domain

Graph Rational Domain - Review on Domain The domain is the...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Review on Domain
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The domain is the set of all input values to which the rule applies. These are called your independent variables . These are the values that correspond to the first components of the ordered pairs it is associated with. If you need a review on domain, feel free to go to Tutorial 30: Introductions to Functions . Example 1 : Give the domain of the function . Our restriction here is that the denominator of a fraction can never be equal to 0. So to find our domain, we want to set the denominator equal to 0 and restrict those values. *The den. cannot equal to 0 *Factoring to help "solve" *1/2 and -3 are restricted values Our domain is all real numbers except 1/2 and -3 , because 1/2 and -3 both make the denominator equal to 0, which would not give us a real number answer for our function. Vertical Asymptote
Background image of page 2
Let be written in lowest terms and P and Q are polynomial functions. If or as , then the vertical line x = a is a vertical asymptote. The line x = a is a vertical asymptote of the graph of f if and only if the denominator Q( a ) = 0 and the numerator . In other words, you find the vertical asymptote by locating where the function is undefined. In this case that is where the simplified rational function’s denominator is equal to 0. Some things to note: or many vertical asymptotes. It will be x = whatever number(s) cause the denominator to be zero after you have simplified the f You draw a vertical asymptote on the graph by putting a dashed vertical (up and down) line going through x = a as shown below. This is where the function is undefined, so there will be NO point on the vertical asymptote itself. The graph will approach it from both sides, but never cross over it. Below is an example of a vertical asymptote of x = 2:
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 2 : Find the vertical asymptote of the function . First we want to check and see if this rational function will reduce down : *Factor the function Nothing is able to cancel out, so now we want to find where the denominator is equal to 0:
Background image of page 4
*Set den = 0 *Set the first factor = 0 *Set the second factor = 0 There are two vertical asymptotes: x = -3 and x = 3. Example 3 : Find the vertical asymptote of the function . First we want to check and see if this rational function will reduce down :
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
*Factor the function *Cancel out the common factor of x + 1 Note how the factor x + 1 canceled out, so now we want to find where the new denominator is equal to 0: *Set den = 0 There is one vertical asymptote: x = -2. Horizontal Asymptote Let be written in lowest terms, where P and Q are polynomial functions and .
Background image of page 6
If as or , then the horizontal line y = a is a horizontal asymptote. If there is a horizontal asymptote, it will fit into one of the two following cases: be written in lowest terms, of P( x ) < the degree of Q( x ), then there is a horizontal asymptote at y = 0 ( x -axis). of P(
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 34

Graph Rational Domain - Review on Domain The domain is the...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online