Transcript QUADRATIC FUNCTIONS

SECTION 1.4
LIBRARY OF FUNCTIONS;
PIECEWISE-DEFINED FUNCTIONS
LINEAR FUNCTIONS
f(x) = mx + b
Domain: Reals
m and b are real
Range: Reals
Graph: Nonvertical straight line with
slope m and y-intercept b
Increasing function if m > 0
Decreasing function if m < 0
CONSTANT FUNCTIONS
f(x) = b
Domain: Reals
b is real
Range: The number b
Graph: Horizontal Line
Y-intercept: (0,b)
Even Function
Graph is constant over its domain.
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 ycoordinates are the same.
Odd function; increasing function.
SQUARE FUNCTION
f(x) = x2
Domain: All Reals
Range: Nonnegative Reals.
Graph:
Parabola
Even Function
Intercept:
(0,0)
Decreasing: (-  , 0)
Increasing: (0, )
CUBE FUNCTION
f(x) = x3
Domain: All Reals
Intercept:
Range: All Reals.
(0,0)
Odd Function
Increasing: (-  , )
CUBE ROOT FUNCTION
f(x) x
3
Domain: All Reals
Intercept:
Range: All Reals.
(0,0)
Odd Function
Increasing: (-  , )
SQUARE ROOT
FUNCTION
f(x) 
x
Domain and Range: Nonnegative Reals.
Intercept:
(0 , 0)
Neither Even nor Odd
Increasing: (0 , )
RECIPROCAL FUNCTION
1
f(x) 
x
Domain and Range: Nonzero Reals.
Intercepts: None
Odd Function
Decreasing: (-  , 0) and (0 , )
ABSOLUTE VALUE
FUNCTION
f(x)  x
Domain: All Reals
Range:
Nonnegative Reals
Intercept:
(0,0)
Even Function
Dec: (-  , 0) Inc: (0 , )
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
GREATEST INTEGER ON
CALCULATOR
Math  Num
Choose Option 5
Then enter number
EXAMPLE:
Graph:
y=[[x]]
Hint: Be sure to use dot mode!
GREATEST INTEGER
FUNCTION
The greatest integer function is
called a piecewise function.
OTHER PIECEWISEDEFINED FUNCTIONS
Graph:
-x+2
if x  2
f(x) =
2 x - 8 if x > 2
OTHER PIECEWISEDEFINED FUNCTIONS
Graph:
- x - 6 if x < - 3
f(x) =
9 - x 2 if - 3  x  3
x - 6 if
x>3
CONCLUSION OF SECTION 1.4