INTRODUCTION TO LINEAR FUNCTIONS

WHAT DID WE LEARN ABOUT FUNCTIONS?

We spent the last unit discussing functions. We found the

independent variable, __, the dependent variable, __,

the __________, the ______, and the ________for the function. This

unit we will be looking at a specific type of function –

___________________.

xy

equation

tablegraph

Linear Functions

SIMILARTIES

Functions Linear Functions

Differences:

Both have tables.Both have graphs.

Both have equations.

Both have a domain and rangeBoth have independent and

dependent variables.

Both can be continuous, the data is connected.

Functions can be discrete, the data is not connected.

WHAT DOES A LINEAR FUNCTION LOOK LIKE ON A GRAPH?

A ________ __________ is a function that on a graph the solutions, ______, are represented by a _________

linear function(x,y)line.

EXAMPLES OF FUNCTIONS:

Is it a function? Then is it a linear or nonlinear function?

Yes, it is a function.The graph is a line. It is a linear function.

Yes, it is a function.The graph is not a line. It is a nonlinear function.

EXAMPLES OF FUNCTIONS:

Is it a function? Then is it a linear or nonlinear function?

Yes, it is a function.The graph is a line. It is a linear function.

Yes, it is a function.The graph is not a line. It is a nonlinear function.

EXAMPLES OF FUNCTIONS:

Is it a function? Then is it a linear or nonlinear function?

Yes, it is a function.The graph is a line. It is a linear function.

No, not a function.

EXAMPLES OF FUNCTIONS:

Is it a function? Then is it a linear or nonlinear function?

No, not a function. Yes, it is a function.The graph is not a line. It is a nonlinear function.

EXAMPLES OF FUNCTIONS:

Is it a function? Then is it a linear or nonlinear function?

Yes, it is a function.The graph is not a line. It is a nonlinear function.

Yes, it is a function.The graph is not a line. It is a nonlinear function.

EXAMPLES OF FUNCTIONS:

Is it a function? Then is it a linear or nonlinear function?

No, not a function.Yes, it is a function.The graph is a line. It is a linear function.

EXAMPLES OF FUNCTIONS:

Is it a function? Then is it a linear or nonlinear function?

Yes, it is a function.The graph is a line. It is a linear function.

Yes, it is a function.The graph is not a line. It is a nonlinear function.

VOCABULARY FOR LINEAR FUNCTIONS

Linear function – function with a graph that is continuous

Linear equation – equation whose graph is a straight line

X intercept – the point where a line crosses the x axis of a graph

Y intercept – the point where a line crosses the y axis

Rate of change – how the steepness of a line is changing

Slope – the steepness of the line on a graph

Slope formula – the formula used to find the slope between two ordered pairs

Slope intercept form – y = mx + b – a form used to graph linear functions

Point slope from – y – y1 = m(x – x1) Domain – the list of all x values Range – the list of all y values Independent variable – the input you choose

for x Dependent variable – the output you get

when you choose the input and apply the function rule

Function rule – the rule that defines the relationship between x and y

Function rule – the rule that defines the relationship between x and y

Positive slope – the line on a graph moves in an upward direction from left to right

Function rule – the rule that defines the relationship between x and y

Positive slope – the line on a graph moves in an upward direction from left to right

Negative slope – the line on a graph moves in a downward graph from left to right

Function rule – the rule that defines the relationship between x and y

Positive slope – the line on a graph moves in an upward direction from left to right

Negative slope – the line on a graph moves in a downward graph from left to right

Zero slope – the slope of a horizontal line

Function rule – the rule that defines the relationship between x and y

Positive slope – the line on a graph moves in an upward direction from left to right

Negative slope – the line on a graph moves in a downward graph from left to right

Zero slope – the slope of a horizontal line Undefined slope – the slope of a vertical

line