Warm UpMar. 12 th  Solve each rational equation or inequality.

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Presentation transcript:

Warm UpMar. 12 th  Solve each rational equation or inequality.

Homework Answers

Graphing Rational Functions You will be able to identify: the domain, the y-intercept, the vertical asymptotes and the end behavior asymptote

Parent Graphs

Domain  Remember: You can’t divide by zero!  All values that make you divide by zero are undefined so we don’t include them in the domain  Examples:

Discontinuities  The values that are not included in the domain cause the graph to be discontinuous – meaning there is a break in the graph  Removeable – Hole – caused by a factor that cancelled out while simplifying  Non-removable – Vertical Asymptote – caused by a factor left in the denominator

Holes & Vertical Asymptotes (VA)

Discontinuities

Y-intercept  To find a y-intercept, plug in x = 0 and simplify.  If 0 is undefined and not included in the domain, then the graph does not have a y-intercept.

X-intercept(s)  After simplifying by finding the holes, set the function equal to 0 and solve for x.

X-intercept(s)

End Behavior Asymptotes ( EBA )  To find the end behavior asymptote simply divide the 2 polynomials… but first, look at the degrees of top and bottom.  Bottom Heavy: degree of the bottom is bigger than the degree of the top  EBA is always y = 0  Equal: degree of the bottom is the same as the degree of the top  EBA is always y = leading coefficient leading coefficient  Top Heavy: degree of the top is bigger than the degree of the bottom  There’s no trick, you have to divide using polynomial division.

Examples  Identify the EBA for each of the following:

Equations from a Graph…  What are the equations of the asymptotes? Describe the equation of the graph.

 What are the equations of the asymptotes?  What is the x-coordinate of the hole? Describe the equation of the graph.

PRACTICE Identify the domain, vertical asymptote(s), x- and y-coordinates of holes, and end behavior asymptotes.