Graph Parameters and Intersections

This video tutorial covers the determination of equations for trigonometric graphs, focusing on parameters a, p, k, and q. It explains how these parameters affect graph transformations, such as vertical and horizontal stretches and shifts. The tutorial also includes a comparison of two graphs, f(x) and g(x), to determine where one graph is greater than the other, using critical points of intersection.

What are the four parameters that can be tested in trigonometric graphs?

• Amplitude, Period, Phase Shift, Vertical Shift

• Height, Width, Depth, Volume

• Slope, Intercept, Curvature, Angle

• Frequency, Wavelength, Speed, Time

How is the parameter 'a' determined for the red graph?

• By measuring the distance between peaks

• By calculating the slope

• By comparing the maximum and minimum values

• By finding the horizontal length

What does the parameter 'p' do to the red graph?

• Stretches it vertically

• Moves it up or down

• Compresses it horizontally

• Moves it left or right

What effect does the parameter 'k' have on the blue graph?

• It changes the amplitude

• It alters the vertical shift

• It affects the horizontal stretch or compression

• It modifies the phase shift

How is the parameter 'q' determined for the blue graph?

• By calculating the slope

• By finding the intersection points

• By measuring the horizontal distance

• By observing the vertical shift

Where should you look to determine where f(x) is greater than g(x)?

• At the points where the graphs intersect

• At the endpoints of the domain

• At the maximum points of each graph

• At the minimum points of each graph

What is the significance of the points A, B, and C in the context of f(x) > g(x)?

• They are the points of maximum height

• They are the endpoints of the graphs

• They are the points of minimum height

• They are the points where the graphs intersect

Why is it important to consider the domain when determining where f(x) > g(x)?

• To ensure the graphs do not extend beyond the given range

• To determine the amplitude of the graphs

• To find the maximum value of the graphs

• To calculate the slope of the graphs

What should you do when you encounter a question about graph intersections?

• Calculate the slope at each point

• Circle the areas where the graphs intersect

• Find the maximum and minimum values

• Measure the distance between peaks

What is the final step in solving for the values of x where f(x) > g(x)?

• Calculate the slope of each graph

• Use x values to explain the answer

• Find the maximum and minimum points

• Determine the amplitude of each graph