4-6 Functions and Linear Equations (pg 177-181)

Standard : PFA

Indicator(s): P1: Represent patterns, rules and functions with words, tables, graphs, and variable expressions.P5: Recognize linear equations by plotting points in the coordinate planeP10: Analyze linear and non-linear relationships to show how changes in one variable results in the change of another

Vocabulary

Function- is an input/output relationship. You put a number in, perform the given function, and see what comes out.

Function table- a table that organizes the input and output for a function

Domain- the values that can go into a function (x)

Range- the values that come out of a function (y)

What is a linear equation? A linear equation has a graph that is a

straight line. A linear equation looks like y=mx + b,

where a and b are positive or negative numbers.

“m” represents the slope of the line (we will discuss this more in the next section)

“b” represents the y intercept (where the graphed line crosses the y axis)

Graphing a linear equation

Select a few values for x.

Substitute and solve for y.

Use each solution to write an ordered pair (x,y).

x 2x +1=y y (x,y)

2 +1=y

2 +1=y

2 +1=y

2 +1=y

(2)

(1)

(0)

(-1)

2

1

0

-1

5

3

1

-1

(2,5)

(1,3)

(0,1)

(-1, -1)

Graphing a linear equation (continued) Plot the points for the

(x,y) pairs. Draw a line through

the points you graphed.

x 2x +1=y y (x,y)

2 2(2)+1=y 5 (2,5)

1 2(1)+1=y 3 (1,3)

0 2(0)+1=y 1 (0,1)

-1 2(-1)+1=y -1 (-1,-1) Notice: the line crosses the y-axis at (0,1)

The four families of functions that you should know…

Family Function(general)

Example Shape of graph

Table change

Linear y=mx +b y = 3x y = -2x +2

Quadratic y=ax2+bx+c

y = x2

y = -2x2

Exponential y =abx y = 3x

y = (1/2)x

inverse y =k x

y = 1 x

The four families of functions that you should know…

Family Function(general)

Example Shape of graph

Table change

Linear y=mx +b y = 3x y = -2x +2

Line Add/Subtract

Quadratic(non-linear)

y=ax2+bx+c

y = x2

y = -2x2

Parabola(U Shape)

Change increases

Exponential(non-linear)

y =abx y = 3x

y = (1/2)x

Curve(half-pipe)

Multiply/divide

Inverse(non- linear)

y =k x

y = 1 x

hyperbola Split graph

x*y =k

To which family do the following belong?

y = 4x Exponential

y = 3x +7Linear

y =Inverse

y = 2x2 – 4Quadratic

x

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