Understanding Inequalities and Square Root Functions

The video tutorial covers graphing square root inequalities, starting with an introduction to the concept. It explains how to find x-intercepts, plot points, and sketch the graph. The tutorial also discusses how to determine shading for the inequality graph and provides a second example to reinforce the learning. The session concludes with a summary of the graphing process.

What is the first step in transitioning from graphing square root functions to inequalities?

• Identifying the y-intercept

• Understanding the inequality symbol

• Finding the slope

• Calculating the vertex

In the inequality Y < √(2x - 6), what does the '-6' represent?

• A reflection

• A horizontal shift

• A vertical shift

• A scaling factor

How do you determine the x-intercept for the inequality Y < √(2x - 6)?

• Set Y to zero and solve for X

• Use the slope-intercept form

• Set X to zero and solve for Y

• Find the midpoint of the graph

What is the x-intercept for the inequality Y < √(2x - 6)?

• X = -3

• X = 0

• X = 6

• X = 3

When plotting points for Y < √(2x - 6), what is the value of Y when X = 4?

• Y = √4

• Y = 2

• Y = √2

• Y = 1

Why is the line for Y < √(2x - 6) dotted?

• Because it represents a boundary that is not included

• Because it is a vertical line

• Because it represents a boundary that is included

• Because it is a horizontal line

How do you determine which side of the line to shade for Y < √(2x - 6)?

• Shade above the line

• Shade below the line

• Shade both sides

• Test a point not on the line

In the new inequality with a left shift, what does adding 5 to the equation indicate?

• A shift to the right

• A reflection

• A shift to the left

• A vertical shift

What is the x-intercept for the new inequality with a left shift?

• X = -5/3

• X = 5/3

• X = 3

• X = 0

When plotting points for the new inequality, what is the value of Y when X = 0?

• Y = √5

• Y = 0

• Y = √3

• Y = 5