definitions of the day (dods) 11.2 – graphing rational functions rational function asymptote
TRANSCRIPT
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Definitions of the Day (DODs)
11.2 – Graphing Rational Functions
• Rational Function
• Asymptote
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Definition: Rational Function:A function that can be written in the form
Examples:
polynomialpolynomial
f x
14
f xx
2
2y
x
2 3 22
x xg x
x
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Definition: A line is an asymptote of a graph if the graph of the function gets closer and closer to the line, but does not cross it.
Example:The red lines are asymptotes.
One line is a vertical asymptote (x = 0).
The other line is a horizontal asymptote (y = 0).
Notice that the graph approaches the asymptotes, but does not cross them.
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Finding Vertical Asymptotes
Evaluate each rational function for x = 3.
14
f xx
2
2y
x
2 3 22
x xg x
x
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Find the vertical asymptote for each rational function.
To find vertical asymptotes, we will set the denominator equal to zero and solve for x.
14
f xx
2
2y
x
2 3 22
x xg x
x
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Steps to graphing a rational function:
1. Find the vertical asymptote. The vertical asymptote is where the denominator equals zero.
2. Make a table of values around the asymptote.
3. Draw the graph (remember to show the asymptote by using a dashed line).
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Graphing a rational function
Graph the function 4
3y
x
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Graphing a rational function
Graph the function 3
2yx
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Your Turn!!Evaluate the rational function for x = -2
61)
1f x
x
Graph the following function
22) y
2x
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Sentence Frames
1. A rational function is a __________ over another ___________.
2. To find a vertical asymptote, I need to _________________________________________.