Graphing Inequalities and Functions

Front

What is the definition of a graphing inequality?

Back

A graphing inequality is a mathematical expression that shows the relationship between two variables, where one variable is not strictly equal to the other, represented visually on a coordinate plane.

Front

What does the symbol '≤' indicate when graphing?

Back

The symbol '≤' indicates that the line is solid, meaning that points on the line are included in the solution set.

Front

What does the symbol '>' indicate when graphing?

Back

The symbol '>' indicates that the line is dotted, meaning that points on the line are not included in the solution set.

Front

How do you determine the solution set of a system of inequalities?

Back

The solution set is determined by finding the region where the shaded areas of the inequalities overlap on the graph.

Front

What is the significance of the equal sign in an inequality?

Back

The equal sign indicates that the boundary line is included in the solution set, resulting in a solid line when graphed.

Front

What is the difference between a solid line and a dotted line in graphing inequalities?

Back

A solid line indicates that the points on the line are part of the solution set (used with ≤ or ≥), while a dotted line indicates that the points on the line are not part of the solution set (used with < or >).

Front

How can you tell if a point is part of the solution set for an inequality?

Back

To determine if a point is part of the solution set, substitute the point's coordinates into the inequality and check if the statement is true.

Front

What is the solution set for the inequality y < 2x + 3?

Back

The solution set includes all points below the line y = 2x + 3, not including the line itself.

Front

What does the term 'boundary line' refer to in graphing inequalities?

Back

The boundary line is the line that represents the equation of the inequality, separating the solution set from the non-solution set.

Front

What is the first step in graphing a linear inequality?

Back

The first step is to graph the corresponding linear equation as if it were an equality.