2.4 Graphs of Functions The graph of a function is the graph of its ordered pairs.

Graphing a Function by Plotting Points

Steps for Graphing an Equation Using a Graphing Utility

Ex 1: Graphing a Function by Plotting Points

Solution x

Solution Contd.

Practice Exercise

Answer

Obtaining Information From Graphs You can obtain information about a function from its graph. At the right or left of a graph, you will find closed dots, open dots, or arrows. An arrow indicates that the graph extends indefinitely in the direction in which the arrow points.

Obtaining Information From Graphs A closed dot indicates that the graph does not extend beyond this point and the point belongs to the graph. An open dot indicates that the graph does not extend beyond this point and the point does not belong to the graph.

Ex 2: Obtaining Information From a Function’s Graph

Solution of part a.

Solution of part b.

Solution of part c.

The Vertical Line Test If any vertical line intersects a graph in more than one point, the graph does not define y as a function of x.

Ex 3: Using the Vertical Line Test

Solution

Increasing Function A function is increasing on an interval if for any x 1 and x 2 in the interval, where x 1 <x 2, then f(x 1 )<f(x 2 ).

Decreasing Function A function is Decreasing on an interval if for any x 1 and x 2 in the interval, where x 1 <x 2, then f(x 1 )>f(x 2 ).

Constant Function A function is constant on an interval if for any x 1 and x 2 in the interval, where x 1 <x 2, then f(x 1 )=f(x 2 ).

Ex 4: Intervals on Which a Function Increases, Decreases, or Is Constant

Solution

Even Function

Odd Function

Identifying Even or Odd Functions

Solution

Solution for part a.

Solution for part b.

Solution for part c.

Even Functions and y-Axis Symmetry

Odd Functions and Origin Symmetry

Graphs of Common Functions Use a graphing utility to verify the following six graphs.

Constant Function Domain: Range: the single number Constant on Even function

Identity Function

Standard Quadratic Function

Standard Cubic Function

Square Root Function

Absolute Value Function

Greatest Integer Function