LIBRARY OF FUNCTIONS

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SECTION 1.4

• LIBRARY OF FUNCTIONS
• PIECEWISE-DEFINED FUNCTIONS

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LINEAR FUNCTIONS
f(x) mx b m and b are real Domain
Reals Range Reals Graph Nonvertical straight
line with slope m and y-intercept b Increasing
function if m gt 0 Decreasing function if m lt 0
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CONSTANT FUNCTIONS
f(x) b b is real Domain Reals Range
The number b Graph Horizontal Line
Y-intercept (0,b) Even Function Graph is
constant over its domain.
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IDENTITY FUNCTION
f(x) x Domain and Range are all reals. Graph
Line with slope 1 Intercept (0, 0) Contains
all points whose x- and y-coordinates are the
same. Odd function increasing function.
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SQUARE FUNCTION
f(x) x2 Domain All Reals Range
Nonnegative Reals. Graph Parabola
Intercept (0,0) Even Function Decreasing (-
? , 0) Increasing (0, ?)
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CUBE FUNCTION
f(x) x3 Domain All Reals Range All
Reals. Intercept (0,0) Odd Function Increasing
(- ? , ?)
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CUBE ROOT FUNCTION
Domain All Reals Range All Reals. Intercept (
0,0) Odd Function Increasing (- ? , ?)
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SQUARE ROOT FUNCTION
Domain and Range Nonnegative
Reals. Intercept (0 , 0) Neither Even nor
Odd Increasing (0 , ?)
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RECIPROCAL FUNCTION
Domain and Range Nonzero Reals. Intercepts
None Odd Function Decreasing (- ? , 0) and (0
, ?)
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ABSOLUTE VALUE FUNCTION
Domain All Reals Range Nonnegative
Reals Intercept (0,0) Even Function Dec (- ?
, 0) Inc (0 , ?)
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GREATEST INTEGER FUNCTION
f(x) x Means the greatest integer less
than or equal to x. Examples 6.4 6
6 6 - 6.4 -7
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GREATEST INTEGER ON CALCULATOR
Math Num Choose Option 5 Then enter number
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EXAMPLE

• Graph
• y x
• Hint Be sure to use dot mode!

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GREATEST INTEGER FUNCTION
The greatest integer function is called a
piecewise function.
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OTHER PIECEWISE-DEFINED FUNCTIONS
Graph - x 2 if x 2 f(x) 2
x - 8 if x gt 2
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OTHER PIECEWISE-DEFINED FUNCTIONS
Graph - x - 6 if x lt - 3 f(x) 9 -
x 2 if - 3 x 3 x - 6 if x gt 3
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• CONCLUSION OF SECTION 1.4