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.Domain of f(x) _________ 2.Range of f(x) _________ 3.f(2) ________ 4.f(0) _________ 5.f(4) _________

Use the graph of g(x) to find: 1.Domain of g: _________ 2.Range of g: _________ 3.f(-2): _________ 4.f(-6): _________ 5.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) = -x 3 + 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

Sketch the graph of f(x) = x 2 + 4x x 2

Sketch the graph of f(x) = 1 – x 2 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.x 3 – 2x 2 2.x 3 + 3x 2 – 1