Write an inequality for each graph.

Name: Problem 41, Chapter 2: Algebra 2
Uploaded: 2020-01-19T22:03:45-08:00
Duration: 3 min 5 s
Channel: Ali Soave
Description: Write an inequality for each graph.

Key Concepts

Linear Inequalities

Linear inequalities involve expressions where two linear expressions are related by an inequality symbol (such as <, >, ?, or ?) rather than an equality sign. They define regions on a number line or coordinate plane that represent all the solutions that satisfy the inequality.

Graphical Representation of Inequalities

Graphing an inequality on the coordinate plane involves drawing a boundary line, which represents where the equality holds, and then shading the region that satisfies the inequality. The chosen shading indicates all points (x, y) that make the inequality true.

Boundary Lines

The boundary line in the graph of an inequality represents the set of points where the expression equals the constant term. A solid boundary line is used if the inequality includes equality (? or ?), while a dashed line is used if the inequality is strict (< or >), indicating that points on the line are not included in the solution.

Test Point Method

The test point method is a common technique for determining which side of the boundary line should be shaded when graphing an inequality. By selecting a point not located on the boundary line and substituting it into the inequality, one can verify whether the point satisfies the relationship, thereby identifying the correct region.

Transcript

00:01 Okay, so i've asked to write the inequality for the graph that i'm seeing.

00:05 I'm looking at this graph, and the first thing i notice is the shape of it.

00:08 It takes the shape of an absolute value v graph.

00:11 So i wrote down the general form of our absolute value graphs when they've been transformed.

00:18 I know that my graph has been transformed because the vertex is not at zero zero.

00:23 Normally my absolute value parent graphs are at zero, but this one has been changed, has been translated.

00:30 So i know that it has been moved up, down, left, right, and i'm going to find what those values are.

00:36 So let's start with translating to the left.

00:40 Looks like my graph has been shifted or moved left, and i know that it has been moved left, since the vertex is now at negative 1 on the x instead of 0 on the x.

00:50 So my age value tells me how many units my graph has been moved, left or right, and so since this graph has been moved left, that means it's going to be a negative.

01:03 And i know it's been moved left 1.

01:06 It's going to be a negative 1.

01:08 And then i have x minus here.

01:12 Then i have my k value.

01:14 And my k value tells me how many units i've moved up or down.

01:18 I have a translation of down from 0 ,0, down 1 on the y value.

01:25 And so my k value must be negative 1.

01:29 I'm going to simplify inside the absolute value lines.

01:32 These two negatives must become a positive.

01:34 So this is going to become x plus 1 in the absolute value lines minus 1.

01:41 This is an inequality...