Graphs of Functional Relationships

Lesson 1: Graphs of Functions and Relations

As you go through the Power Point be sure to take some notes on notebook paper.

Intercepts

• The y-intercept of a function is the value of y when x = 0

• If the graph crosses the y-axis at 4, how would you write the ordered pair?

• An x-intercept of a function is a value of x when y = 0

• If the graph crosses the x-axis at -2, how would you write the ordered pair? 

Given the equation y=mx+b

• From what you have learned previously, what does "m" and "b" represent? 

• If m=0, how does this change the graph? Would the graph be linear? Explain your answer.

• Would the graph be a function? How would you know?

• How does the graph of y= 3x + 5 change when x=0?

Properties of a Linear Function

• The graphs are straight lines

• The value of "m" determines the "steepness" of the graph

• The value of "b" tells where the graph crosses the y-axis

• If you start at any point on the graph and run along in a positive direction, then rise up (or down) to another point on the graph, then the ratio rise/run will be constant... no matter what two points you pick.

What would be the domain and range of a linear function?

What is the domain and range of x = 3?

The graph of y = -3 is horizontal

State the domain and range of the graph of y = -3

How do you know when a relation is a function?

• A relation is a set of ordered pairs.

• Any set of ordered pairs relating two variables is called a relation.

• A function is a relation for which there is "exactly one" value of the dependent variable ( input or x-values) for each value of the independent variable (output or y-values).

True or False?

• All relations are function  __________

• All functions are  relation __________

Is y - 4 = 2 ( x - 5 ) a relation?

Is its graph a function?