Problem 9 - Precalculus with Limits

Question

In Exercises 5-18, sketch the graph of the inequality. $$y>-7$$

Step-by-Step Solution

Answer

Graph a dashed horizontal line along \(y = -7\) and shade the area above this line. This area represents all values of \(y\) that are greater than -7.

Step 1: Identify the inequality to be graphed

Here the inequality is \(y > -7\). This inequality tells us that the line to be drawn is along \(y = -7\).

Step 2: Sketch the line

Draw a horizontal line along \(y = -7\). Since \(y\) is strictly greater than -7, make a dashed line to show that points on \(y = -7\) are not included in the solution.

Step 3: Determine the area to be shaded

The inequality is \(y > -7\), therefore the area above the line \(y = -7\) is shaded to show all the \(y\) values greater than -7.

Key Concepts

Inequality Graphing

Graphing inequalities is a way of visually representing the solutions to inequality equations. Let's start with the basics: an inequality indicates the relationship between two values, showing that one is larger or smaller than the other. Unlike equations, which show equality (or the exact point where two expressions meet), inequalities show a range of possible solutions.

To graph an inequality involving a variable such as 'y', we begin by representing the