CHAPTER 8 SECTION 4 GRAPHING RATIONAL FUNCTIONS Algebra
CHAPTER 8 SECTION 4 : GRAPHING RATIONAL FUNCTIONS Algebra 2
Graph by finding the following: *Vertical Asymptote(s), if any: Set the denominator = 0 and solve. *Horizontal Asymptote(s), if any. Compare the degree of the numerator (m) to the degree of the denominator (n). m < n: HA is y = 0 m = n: HA is (Leading coefficient of the numerator / LC of the denominator) m > n: HA does not exist *y-intercept: Let x = 0 and solve. *x-intercept(s): Set the numerator = 0 and solve for x. *Choose other x-values, 2 on each side of an asymptote.
Example 1: What are the asymptotes of the function
Example 2: What are the asymptotes of the function
Example 3: Graph the function, then state the domain and range and any asymptote equations. a)
Example 3: Graph the function, then state the domain and range and any asymptote equations. b)
Example 3: Graph the function, then state the domain and range and any asymptote equations. c)
In some cases, graphs of rational functions may have point discontinuity, which looks like a hole in the graph. This is because the graph is undefined at that point.
Example 4: What is the point of discontinuity of the following functions? a)
Example 4: What is the point of discontinuity of the following functions? b)
Example 4: What is the point of discontinuity of the following functions? c)
Example 5: Graph
Example 6: Graph
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