Graphing Inequalities and Boundaries

The video tutorial explores the representation of algebraic equations and inequalities both visually and algebraically. It begins with plotting on a number line and transitions to using a Cartesian plane for two-dimensional representation. The tutorial explains the concept of boundary lines, the use of dotted lines, and how to test points to determine if they satisfy an inequality. It concludes with identifying solution regions and provides an example using a quadratic inequality.

What is the visual representation of the equation y = 3 on a number line?

• A line through 3

• A hollow circle at 3

• A filled dot at 3

• An arrow starting at 3

When transitioning from a number line to a Cartesian plane, what does the boundary of an inequality represent?

• A filled circle

• A dotted line

• A solid line

• An arrow

If x = 0 and y = 0, does this point satisfy the inequality y > 2x - 1?

• Yes, because 0 = -1

• No, because 0 = 0

• No, because 0 < -1

• Yes, because 0 > -1

What does a dotted line on a graph indicate in terms of inequality solutions?

• The line is included in the solution

• The line is a boundary for equations only

• The line is not included in the solution

• The line represents an asymptote

In the context of graphing inequalities, what does shading a region on a Cartesian plane signify?

• The region contains all possible solutions

• The region is excluded from the solution

• The region is irrelevant to the solution

• The region is a boundary

What is the boundary equation for the inequality y > 2x - 1?

• y = 2x - 1

• y > 3

• y < 2x - 1

• y = 3

How do you determine if a point is a solution to an inequality on a graph?

• By checking if it lies on the boundary line

• By substituting the point into the inequality

• By checking if it is to the right of the y-axis

• By seeing if it is above the x-axis

What is the boundary for the inequality y < x^2?

• y < 2x

• y = 2x

• y > x^2

• y = x^2

When graphing y < x^2, why is the boundary drawn as a dotted line?

• Because the boundary is included

• Because it is a solid line

• Because the boundary is not included

• Because it represents an asymptote

What should you do after drawing the boundary for an inequality like y < x^2?

• Shade the region below the boundary

• Erase the boundary

• Shade the region above the boundary

• Draw a solid line through the boundary