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) = -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 x < 0 -3/2 x 0 < x < 2

3 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