1. 4-6 Functions and Linear Equations (pg 177-181)
Gross 4-6 Notes
4-6 Functions and Linear Equations (pg )
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 plane
P10: Analyze linear and non-linear relationships to show how changes in one variable results in the change of another

2. 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)

3. 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)

4. Graphing a linear equationx
2x +1=y y
(x,y) =y =y
Select a few values for x.
Substitute and solve for y.
Use each solution to write an ordered pair (x,y). 2 1 -1
(2) 5
(2,5)
(1) 3
(1,3) 1
(0)
(0,1) -1
(-1)
(-1, -1)

5. 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)
2(0)+1=y
(0,1) -1
2(-1)+1=y
(-1,-1)
Notice: the line crosses the y-axis at (0,1)

6. 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 = (1/2)x
inverse
y =k x
y = 1

7. 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
y =abx
y = (1/2)x
Curve
(half-pipe)
Multiply/
divide
Inverse
(non- linear)
y =k x
y = 1
hyperbola Split graph
x*y =k

8. y = 4x Exponential y = 3x +7 Linear y = Inverse y = 2x2 – 4 Quadratic
To which family do the following belong?
y = 4x
Exponential
y = 3x +7
Linear
y =
Inverse
y = 2x2 – 4
Quadratic