NOTES 4.2– PATTERNS AND LINEAR FUNCTIONS

A DEPENDENT variable changes in response to another variable.  

The INDEPENDENT variable determines the outcome of the dependent variable.

The values of the independent variable are called INPUTS(x).

The values of the dependent variables are called OUTPUTS(y).

 

In an equation the ANSWER is the dependent variable or output.

Geometric Relationships: For each diagram, find the relationship between the number of shapes and the perimeter of the figure they form. Represent this relationship using a table, words, an equation, and a graph.

What is the independent variable?

What is the dependent variable?

6 7 810

n + 2

TRIANGLES

PERIMETER

Words:  

Equation:   

THE PERIMETER IS 2 MORE THAN THE NUMBER OF TRIANGLES

Graph:

P = T + 2

The perimeter is a FUNCTION of the number of triangles.

PE

RIM

ET

ER

(P

)

TRIANGLES (T)

A function pairs one input with ONE AND ONLY ONE output.

Is the relation described in the first example a function? Why or why not?

 

How would you describe the resulting graph?

A LINEAR function is a function whose graph is a NON-VERTICAL line or part of a non-vertical line.

YES. FOR EACH TRIANGLE THERE IS ONLY ONE PERIMETER.

LINEAR

For each table, determine whether the relationship is a function. Then represent the relationship using words, an equation, and a graph.

YES: For every increase in x, y increases by 2.

YES: For every increase in x, y increases by 1.

Based on the table of data below, what is the independent value? Dependent value? Is it a function? Justify your answer.

Is this a linear relationship? Why or why not?

x 1 3 3 5 6 7

y 2 5 7 8 4 1

INDEPENDENT: x; DEPENDENT: y

NOT A FUNCTION: 3 has two different y-values

NOT LINEAR: 3 has two different y-values; y increases and then decreases.

HOMEWORK: 4.2 pages 259-261 #’s 6-16, 19-22