Understanding Graphical Inequalities

The video tutorial explains how to solve the inequality F(x) < G(x) using a graph. F(x) is represented by a blue line with a negative slope, and G(x) by a red line with a positive slope. The solution involves finding the x-values where F(x) is below G(x). The tutorial identifies the intersection point at x = 2 and explains that the solution is for x > 2. It also covers how to express this solution using inequalities and interval notation.

What is the main objective when solving F(x) < G(x) graphically?

• To find where F(x) is above G(x)

• To find where F(x) is below G(x)

• To find where F(x) is equal to G(x)

• To find where G(x) is below F(x)

What is the significance of the intersection point of the two lines?

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

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

• It shows where F(x) equals G(x)

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

At which x-coordinate do the graphs of F(x) and G(x) intersect?

• x = 4

• x = 2

• x = 0

• x = -2

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

• Nowhere on the graph

• To the left of the intersection point

• To the right of the intersection point

• At the intersection point

Why is the intersection point not included in the solution for F(x) < G(x)?

• Because the intersection point is a minimum

• Because the intersection point is a maximum

• Because the intersection point is irrelevant

• Because the inequality is less than, not less than or equal to

How is the solution graphically represented on the number line?

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

• With an open point on 2 and an arrow to the right

• With an open point on 2 and an arrow to the left

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

What inequality represents the solution to 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 the interval notation for the solution open at 2?

• Because 2 is included in the solution

• Because 2 is not included in the solution

• Because the interval is finite

• Because the interval is closed

What does the interval (2, ∞) represent in the context of this problem?

• All x-values less than 2

• All x-values greater than 2

• All x-values equal to 2

• All x-values less than or equal to 2