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7.4_Linear_Reciprocal_Functions.notebook
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November 30, 2016
McGrawHill Ryerson
PreCalculus 11
Chapter 7Absolute Value and Reciprocal Functions
7.4_Linear_Reciprocal_Functions.notebook
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Focus On ...
Chapter 7 7.4 Reciprocal Functions
• graphing the reciprocal of a given function• analysing the graph of the reciprocal of a given function• comparing the graph of a function to the graph of the reciprocal of that function• identifying the values of x for which the graph of has vertical asymptotes
7.4_Linear_Reciprocal_Functions.notebook
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Review What is a reciprocal?
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For the following reciprocal functions, what are some non permissible values?
f(x) = x and it's reciprocal y = 1 y = 1 f(x) x
7.4_Linear_Reciprocal_Functions.notebook
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For the following reciprocal functions, what are some non permissible values?
f(x) = 2x + 1 and it's reciprocal y = 1 y = 1 f(x) 2x+1
f(x) ≠0 and 2x +1 ≠0
7.4_Linear_Reciprocal_Functions.notebook
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f(x) = 2x + 1 and it's reciprocal y = 1 y = 1 f(x) 2x+1
f(x) ≠0 and 2x +1 ≠0
The reciprocal function will never pass through the lines
7.4_Linear_Reciprocal_Functions.notebook
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An asymptote is an imaginary line that a function can approach but never passes through.
A horizontal asymptote occurs in a reciprocal function at y = 0
A vertical asymptote occurs in a reciprocal function for the nonpermissible value of x (the value of x that makes the denominator zero)
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For the following reciprocal function, what are some non permissible values?
reciprocal
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What points do both the function and reciprocal function both have?
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Points that lie on both the function and it's reciprocal are called Invariant PointsWhat values of y do these occur at?
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Important Characteristics of y = x and its reciprocal
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7.4
Example 1: Your TurnCreate a table of values and sketch the graphs of y = f (x) and its
reciprocal , where f (x) = –x. Examine how the functionsare related.
Table of V
alues
Graphs
Characteristics
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Example
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c) Graph the reciprocal function without using a table of values
3)Determine the invariant points (the points where y = 1 or y = 1)
4)Use this info to graph the reciprocal function
1)Graph the function y = 2x + 1
2) Draw the asymptotes
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7.4
Example 2: Your TurnConsider f (x) = 3x – 9.a) Determine its reciprocal function .
b) Determine the equation of the vertical asymptote of the reciprocal function.c) Graph the function y = f (x) and its reciprocal function ,
with and without technology. Discuss the behaviour of as it nears its asymptotes.
Answer