Graph Intersection and Inequalities

The video tutorial explains how to read solutions from graphs using two methods: the intersection of graphs method and the x-intercept method. It covers how to determine where two functions intersect, where one function is less than or greater than another, and how to find x-intercepts. The tutorial emphasizes understanding these concepts graphically without needing explicit function equations.

What are the two methods discussed for reading solutions off graphs?

• Matrix and determinant

• Derivative and integral

• Slope and y-intercept

• Intersection of graphs and x-intercept

In the intersection of graphs method, what does the intersection point represent?

• Where the functions have the same y-value

• Where the functions have the same derivative

• Where the functions have the same x-value

• Where the functions have different slopes

When solving f(x) = g(x) using the intersection method, what are you finding?

• All x-values where f and g are equal

• All y-values where f and g are equal

• All points where f is above g

• All points where f is below g

What is the solution to f(x) = g(x) if they intersect at (5, 3)?

• y = 3

• y = 5

• x = 5

• x = 3

What does f(x) < g(x) mean in terms of graph position?

• f is above g

• f is to the left of g

• f is below g

• f is to the right of g

In interval notation, how is the solution to f(x) < g(x) represented if it occurs to the right of x = 5?

• (-∞, 5)

• (5, ∞)

• (5, ∞]

• [5, ∞)

What does f(x) ≥ g(x) indicate about the graph of f?

• f is below or equal to g

• f is to the right of g

• f is above or equal to g

• f is to the left of g

How is the solution to f(x) ≥ g(x) expressed in interval notation if it occurs from -∞ to 5?

• (-∞, 5)

• [5, ∞)

• (-∞, 5]

• (-∞, 5)

What is the focus of the x-intercept method?

• Finding the slope of the graph

• Finding where the graph crosses the x-axis

• Finding where the graph crosses the y-axis

• Finding the area under the graph

In the x-intercept method, what does f(x) = 0 represent?

• The maximum point

• The x-intercept

• The y-intercept

• The slope