Understanding Graphical Inequalities

The video tutorial explains how to solve the inequality F(x) > G(x) graphically. It begins by identifying the intersection point where F(x) equals G(x) and then determines the x-values where F(x) is greater than G(x). The solution is represented graphically on the x-axis and expressed using inequalities and interval notation.

What is the primary goal when solving F(x) > G(x) graphically?

• To find where F(x) equals G(x)

• To find where F(x) is above G(x)

• To find where F(x) is below G(x)

• To find where G(x) is above F(x)

What is the significance of the intersection point in the context of F(x) and G(x)?

• It shows where F(x) is greater than G(x)

• It shows where F(x) is less than G(x)

• It shows where F(x) equals G(x)

• It shows where G(x) is greater than F(x)

At what x-coordinate do F(x) and G(x) intersect?

• x = 0

• x = -1

• x = -2

• x = 2

Where is F(x) greater than G(x) on the graph?

• To the right of the intersection point

• To the left of the intersection point

• At the intersection point

• Nowhere on the graph

Why is the point at x = -2 not included in the solution set?

• Because it is outside the graph

• Because F(x) is less than G(x) there

• Because F(x) equals G(x) there

• Because G(x) is greater than F(x) there

How is the solution represented on the x-axis?

• With a closed point at -2 and an arrow to the left

• With an open point at -2 and an arrow to the right

• With an open point at -2 and an arrow to the left

• With a closed point at -2 and an arrow to the right

What inequality represents the solution set for F(x) > G(x)?

• x = -2

• x < -2

• x > -2

• x ≥ -2

How is the solution expressed in interval notation?

• [-∞, -2)

• (-∞, -2]

• (-∞, -2)

• (-∞, -2]

Why is a parenthesis used in the interval notation for -2?

• Because it is a closed interval

• Because -2 is included in the interval

• Because it is an open interval

• Because -2 is not included in the interval

What does the interval (-∞, -2) represent in the context of the graph?

• The region where G(x) is greater than F(x)

• The region where F(x) is greater than G(x)

• The region where F(x) equals G(x)

• The region where F(x) is less than G(x)