linear inequalities b. davis b. davis mathscience innovation center

Linear Inequalities

B. DavisB. Davis

MathScience Innovation CenterMathScience Innovation Center

Linear Inequalities B. Davis MathScience Innovation Center

We started studying functions…

11stst: we defined relations: we defined relations 22ndnd: we specified which relations are : we specified which relations are

functions using lists, mappings, and graphsfunctions using lists, mappings, and graphs 33rdrd: we looked at special functions:: we looked at special functions:

one-to-oneone-to-one constantconstant linearlinear


Straight lines - all 4 kinds

vertical : are relations, not functionsvertical : are relations, not functions horizontal: special linear functions called horizontal: special linear functions called

“constant” where m = 0.“constant” where m = 0. diagonal: linear with positive or negative diagonal: linear with positive or negative

slopeslope All All linear functionslinear functions have the form have the form y=mx + b where m is__________ and b is y=mx + b where m is__________ and b is

________________________________slopeslope

y-intercepty-intercept


The Linear Family of Functions

Any function with x raised to the first Any function with x raised to the first power is related to the power is related to the Linear FamilyLinear Family

y = m x + by = m x + b y = |x| or y = abs ( x )y = |x| or y = abs ( x ) y = [ x ] or y = int (x)y = [ x ] or y = int (x) y > mx + by > mx + b yy < < mx + b mx + b

Linear Equation

Absolute Value Function

Greatest Integer Function

Linear Inequality


Which are linear functions ?

1.1. y =5 x – 9y =5 x – 9

2.2. yy22 – 5 = 8x – 5 = 8x

3.3. y = 5/xy = 5/x

4.4. 5x + y = 195x + y = 19

5.5. y = y =

1 and 4 only

3x


Linear Inequalities are not functions but they are bordered by linear functionsbut they are bordered by linear functions For linear inequalities in 2 variables, a For linear inequalities in 2 variables, a

dotted line is to a _______________ of a dotted line is to a _______________ of a linear inequality in 1 variable.linear inequality in 1 variable.

For linear inequalities in 2 variables, a solid For linear inequalities in 2 variables, a solid line is to a _______________ of a linear line is to a _______________ of a linear inequality in 1 variable.inequality in 1 variable.

open dotopen dot

closed dotclosed dot


y > 2 x + 3 use a dotted line to draw y = 2x +3use a dotted line to draw y = 2x +3 then shade above the line, since y >then shade above the line, since y > use a test point to be sure!use a test point to be sure! on the calculator use y =on the calculator use y =

6

4

2

-2

-4

-5 5 10

f x = 2x+3


y < 2 x + 3 use a solid line to draw y = 2x +3use a solid line to draw y = 2x +3 then shade below the line, since y <then shade below the line, since y < use a test point to be sure!use a test point to be sure! on the calculator use y =on the calculator use y =

6

4

2

-2

-4

-5 5 10

f x = 2x+3

linear inequalities b. davis b. davis mathscience innovation center

Documents