SECTION 1.6 RECIPROCAL OFQUADRATIC FUNCTIONS
i) Concept of Reciprocal Functions
ii) Asymptotes, Invariant Points,
iii) Graphing the Reciprocal of Linear and QF
iv) Domain and Range
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I) WHAT IS A RECIPROCAL ?
A reciprocal is a number you get when switching the valueof the numerator (Top) with the denominator (Bottom).
Ex: Find the reciprocal of each number:
Notice that the reciprocal of 1 and – 1 will stay the same
The reciprocal of 0 is undefined
The reciprocal any value between1 and – 1 will become larger
The reciprocal any value larger than 1 will be smaller
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When finding the reciprocal of a function, put thefunction in the denominator and place a “1” above it
II) THE RECIPROCAL OF A FUNCTION?
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III) GRAPHING RECIPROCAL FUNCTIONS
The reciprocal function takes the reciprocal of all they-coordinates of a function
When graphing a reciprocal function, there are athree main steps:
The reciprocal of 1 or -1 will be the same, so pointswith a y-coordinate of 1 will not change
The reciprocal of zero is undefined, so points with ay-coordinate of zero will become a vertical asymptote
Take the reciprocal of all y-coordinates to find wherethe points of the new function is.
Reciprocal of large numbers become small
Reciprocal of small numbers become large
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EX#1) GRAPH
1. First graph the line:
2. Find X-intercept (when y = 0) Vertical Asymptotes
3. Find Common Points:Points where the Y-coordinate is 1 or -1
y = 0.5x+1
4. Take the reciprocal of theY coordinate for every point
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PRACTICE: GIVEN THE FOLLOWING GRAPH, DRAWTHE RECIPROCAL FUNCTION
x
y
-5
0
5
-5
5
Find the x-intercept VerticalAsymptote
Find common points with a
Y-coordinate of 1 or -1
Pick some points on the original
Function and take the reciprocal
of the Y-coordinate
Reciprocal of large numberswill become small
Reciprocal of small numbers
will become large
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PRACTICE: GRAPH THE FOLLOWING
x
y
-5
0
5
-5
5
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Graph
Find X-intercept Asymptotes
Find the Common Points whereY coordinate is 1 or -1.
Pick some points on the original
Function and take the reciprocal
of the Y-coordinates.Reciprocal of large numberswill become small
Reciprocal of small numbers
Will become large
x
y
-5
0
5
-5
5
GRAPH THE RECIPROCAL OF EACH PARABOLA
x
y
-5
0
5
-5
5
Use the first x-intercept to draw the
Vertical asymptote
Plot the invariant points
Graph each side of the asymptote
There are no x-intercepts, so no VA
Only one invariant point
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EX#) GIVEN THE FOLLOWING GRAPH F(X), GRAPH THERECIPROCAL FUNCTION.
Find X-interceptAsymptotes
Find Common Points
Near to Far &Far to Near
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GIVEN THE FOLLOWING FUNCTION, INDICATE THEDOMAIN AND RANGE:
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