Linear Functions January 11, 2017

Outline Essential Questions Vocabulary review Identifying a linear function by a graph Identifying a linear function by ordered pairs Examples Graphing linear functions Outline

How do I identify a linear function from a graph and from ordered pairs? How do I graph a linear function? Essential Questions

Identifying a linear function by a graph Types of graphs Linear function Not a linear function Not a function Identifying a linear function by a graph

Identifying a linear function by a graph Straight line Passes vertical line test

Identifying a linear function by a graph Not a linear function Identifying a linear function by a graph Not a straight line Passes vertical line test

Identifying a linear function by a graph Not a function Identifying a linear function by a graph Not a straight line Fails vertical line test

Identifying a linear function by a graph Not a function Identifying a linear function by a graph A straight line Fails vertical line test

Identifying a linear function by using ordered pairs Types Linear function Not a linear function Identifying a linear function by using ordered pairs

Identifying a linear function by using ordered pairs Types Linear function Not a linear function Identifying a linear function by using ordered pairs

Identifying a linear function by using ordered pairs Constant rate of change in x values and y-values No repeating y-values Identifying a linear function by using ordered pairs

Identifying a linear function by using ordered pairs YES Identifying a linear function by using ordered pairs x y -2 7 -1 4 1 2 -5 -3 +1 -3 +1 +1 -3 +1 -3

Identifying a linear function by using ordered pairs NO Identifying a linear function by using ordered pairs x y -2 6 -1 3 2 1

Identifying a linear function by using ordered pairs NO Linear function {(-10,10), (-5,4), (0,2), (5,0)} Identifying a linear function by using ordered pairs x y -10 10 -5 4 2 5 -6 +5 -2 +5 +5 -2

YES Linear function Examples {(0,-3), (4,0), (8,3), (12,6), (16,9)} x -3 4 8 3 12 6 16 9

NO Linear function Examples

NO Linear function Examples

NO Linear function Examples {(-4,13), (-2,1), (0,-3), (2,1), (4,13)} x y -4 13 -2 1 -3 2 4

YES Linear function Examples

Graphing linear functions Make sure equation is in slope- intercept form. Plug in x-value Solve for y-value or f(x) After completing chart, graph function. Graphing linear functions

Graphing linear functions f(x) = -3x+4 Graphing linear functions x -2 2 3 4 f(x) 10 -5 -8 f(x) = -3(-2)+4 =6+4 =10 f(x) = -3(2)+4 =-6+4 =-2 f(x) = -3(4)+4 =-12+4 =-8 f(x) = -3(0)+4 =0+4 =4 f(x) = -3(3)+4 =-9+4 =-5

Graphing linear functions f(x) = -3x+4 Graphing linear functions x -2 2 3 4 f(x) 10 -5 -8

Graphing linear functions f(x) = x+7 Graphing linear functions x -5 -4 -2 1 f(x) 2 3 5 7 8 f(x) = (-5)+7 =-5+7 =2 f(x) = (-2)+7 =-2+7 =5 f(x) = (1)+7 =1+7 =8 f(x) = (-4)+7 =-4+7 =3 f(x) = (0)+7 =0+7 =7

Graphing linear functions f(x) = x+7 Graphing linear functions x -5 -4 -2 1 f(x) 2 3 5 7 8

Graphing linear functions f(x) = 5x Graphing linear functions x -5 -3 3 5 f(x) -25 -15 15 25 f(x) = 5(-5) =-25 f(x) = 5(0) =0 f(x) = 5(5) =25 f(x) = 5(-3) =-15 f(x) = 5(3) =15

Graphing linear functions f(x) = 5x Graphing linear functions x -5 -3 3 5 f(x) -25 -15 15 25