1.3
Graphs of Functions
• Equations are mathematical ___________________________.
• ______________________ are what make the sentences true.
• A ________________ is a picture of the solutions.
Graphs can be done by hand or with the graphing
utility (AKA, GUT)
Domain and Range
• Domain is the set of ___ values that are included in a function. This is
also the directed distance from the ____ axis.
• Range is the set of ____ values that are included in a function. This is
also the directed distance from the ____ axis.
Use the graph of f(x) to find:
1.
2.
3.
4.
5.
Domain of f(x)
_________
Range of f(x)
_________
f(2)
________
f(0)
_________
f(4)
_________
Use the graph of g(x) to find:
1.
2.
3.
4.
5.
Domain of g:
_________
Range of g:
_________
f(-2):
_________
f(-6):
_________
f(1):
_________
Increasing, Decreasing, Constant
• To determine if a function is increasing, decreasing or constant, the
graph should be read from __________ to _________.
• You must state the _____________ for which the y values are
increasing, decreasing, or constant.
Determine the intervals that the function below is
increasing, decreasing or constant.
• Increasing: _______________
• Decreasing: ______________
• Constant: _______________
Determine the intervals that the function below is
increasing, decreasing, or constant.
• Increasing: _______________
• Decreasing: ______________
• Constant: _______________
Use your GUT to approximate the relative max and
min of f(x) = -x3 + x. Then determine the intervals
the function is increasing, decreasing, or constant.
Piece- wise functions
• A piece wise function is a function that is defined by two or
more equations over a specified domain.
• To sketch the graph of a piece wise function, you need to
sketch the graph of each equation on the appropriate portion
of the domain.
Sketch the graph of f(x) = 2x + 3 x < 1
-x + 4
x>1
Sketch the graph of f(x) = x2 + 4x
-3/2 x
3
x<0
0<x<2
x>2
Sketch the graph of f(x) = 1 – x2
x<1
2
1<x<3
2x – 4
x>3
Exit Pass
Determine the intervals over which the functions are increasing,
decreasing, or constant. Then find any relative maximum and
minimum values.
1. x3 – 2x2
2. x3 + 3x2 – 1