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Absolute Value Functions Part 1 April 12, 2013
McGraw-Hill Ryerson
Pre-Calculus 11
Chapter 7Absolute Value and Reciprocal Functions
Absolute Value Functions Part 1 April 12, 2013
McGraw-Hill Ryerson Pre-Calculus 11
Teacher Notes1. This lesson is designed to help students conceptualize the main ideas of Chapter 7.
2. The lesson was written using SMART Notebook 10.0. Other versions of the software do not offer the same functionality.
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Absolute Value Functions Part 1 April 12, 2013
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
Absolute Value Functions Part 1 April 12, 2013
2
1
2
7.4Example 1
1 Use a table of values to graph the functions y = x and .
Compare the Graphs of a Function and Its Reciprocal
Sketch the graphs of y = f (x) and its reciprocal function , wheref (x) = x. Examine how the functions are related.
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Absolute Value Functions Part 1 April 12, 2013
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7.4 Example 1 Continued
44
3 The function y = x is a function of degree one, so its graph is a line.
The function is a rational function.
Absolute Value Functions Part 1 April 12, 2013
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.
Tabl
e of
Val
ues
Gra
phs
Cha
ract
eris
tics
Absolute Value Functions Part 1 April 12, 2013
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1
2 b) A vertical asymptote occurs at any non-permissible values of the
corresponding rational expression .
7.4Example 2
1 a) The reciprocal function is .
Graph the Reciprocal of a Linear FunctionConsider f (x) = 2x + 5.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 .
Describe a strategy that could be used to sketch the graph of a reciprocal function.
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Absolute Value Functions Part 1 April 12, 2013
3 To determine non-permissible values, set the denominator equal to 0 and solve.2x + 5 = 0 2x = –5
x = –
In the domain of the rational expression , .
The reciprocal function is undefined at this value, and its graph
has a vertical asymptote with equation x = .
3
4 The graphs of y = 2x + 5 and
are shown.
4
7.4 Example 2 Continued
Absolute Value Functions Part 1 April 12, 2013
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
