Representations of Inequalities

Table of Contents 41: How Do I Represent Inequalities in Different Ways? 40: Warm-Up, Guided Practice Worksheet

Warm Up What are the four representations of functions and what do they mean?

Learning Intention/Success Criteria LI: We are learning to write inequalities in four representations. SC: I know how to -represent inequalities in 4 ways: symbolically, visually, set notation, and verbally -recognize and compare slope from a graph -write inequalities describing when one graph is larger than another.

EQ: How Do I Write Inequalities in Different Ways? 11/10/2018

Inequality A mathematical sentence built from expressions using one or more of the following symbols: < > ≤ ≥ Less Than Greater Than Less Than or Equal To Greater Than or Equal To

● Closed Circle Used to represent the inequality greater than or equal to OR less than or equal to. The point is part of the solution ○ Open Circle Used to represent the inequality greater than OR less than. The point is NOT part of the solution

Four Ways to Represent Inequalities 1. Symbolically Writing an inequality with inequality signs (<, >, ≥, or ≤) Also know as symbolic notation Examples: x > 3 2 < k ≤ 40 g ≤ 6

2. Visually Graphing inequalities on a number line or coordinate grid An open circle with an arrow or a dotted line is used if the inequality is less than OR greater than A closed circle with an arrow or a solid line is used if the inequality is less than or equal to OR greater than or equal to

3. Set Notation Writing inequalities with brackets Written in the form: { variable : symbolic notation } { } = brackets; shows this is a set Variable = the variable you are using : = “such that”

Example: { x : x > 3} Spoken: the set of all x’s such that x is greater than 3

4. Verbally Using words to describe the inequality Example: x is greater than 3

Example 1: Write the inequality in 4 representations of inequalities Symbolic: Visual: Set: Verbal: m > 7 5 6 7 8 9 10 { m : m > 7} All values m greater than 7

Guided Practice For each row, fill in the missing columns to show different ways of representing the same inequality., Then, in the last column, circle all values that are solutions to the inequality represented in that row.

Guided Practice 1a Symbolic Notation: Verbal Description: Set Notation: Line Graph: Possible Solutions: k > 3 All values of k greater than 3 { k : k > 3 } 1 2 3 4 5 6 9 6 12

Guided Practice 1b Symbolic Notation: Verbal Description: Set Notation: Line Graph: Possible Solutions: g ≤ 2 All values g less than or equal to 2 { g : g ≤ 2 } 1 2 3 4 5 6 -2 ½ -8/3 0 -3

Guided Practice 1c Symbolic Notation: Verbal Description: Set Notation: Line Graph: Possible Solutions: d < 2/3 All values d less than 2/3 { d : d < 2/3 } 0 1 -2 ½ -8/3 0 -3

Guided Practice 1d Symbolic Notation: Verbal Description: Set Notation: Line Graph: Possible Solutions: x ≥ -1 All values x greater than or equal to -1 { x : x ≥ -1 } -4 -3 -2 -1 0 1 9 ½ 6 0 12

Example 2: Use the graph of the linear functions to answer questions

Which is greater, f(2) or g(2)? How do you know? f(2) is greater than g(2). I know this because f(2) = 3 and g(2) = 1. Since 3 is bigger than 1, f(2) is greater. For which value of x is f(x) = g(x)? f(x) is equal to g(x) when x = 1.

For which values of x is f(x) ≥ g(x)? Write your answer in set notation. { x : x ≥ 1 } For which values of x is f(x) < g(x)? Write your answer in set notation. { x : x < 1 }

Guided Practice 2 a) Is f(-4) < g(-4)? Explain how you can tell b) For which values of x is it true that f(x) ≤ g(x)? Write your answer in set notation c) For which values of x is it true that f(x) ≥ g(x)? Show the solution on a number line.

Guided Practice 2 Answers a) g(-4) is larger than f(-4). You can tell by inferencing how the linear graphs would continue b) { x : x ≤ -3 } c) -3