Transformations of Functions and Graphs

The video tutorial guides students through solving an SAT math question involving graph translations. It explains how to determine the equation for G(x) in terms of F(x) by analyzing horizontal and vertical shifts. The tutorial demonstrates eliminating incorrect options and verifies the solution using a graphing calculator.

What is the main objective of the SAT math question discussed in the video?

• To solve a system of linear equations

• To determine the equation of G(x) in terms of F(x)

• To calculate the area under a curve

• To find the value of x in a quadratic equation

How is the function F(x) transformed horizontally to become G(x)?

• Shifted left by two units

• Shifted right by two units

• Shifted up by two units

• Shifted down by two units

What is the effect of adding a positive constant to F(x) in terms of vertical translation?

• The graph shifts down

• The graph shifts up

• The graph remains unchanged

• The graph reflects over the x-axis

Which of the following equations represents a shift of F(x) right by two units?

• F(x) - 2

• F(x) + 2

• F(x - 2)

• F(x + 2)

What is the correct equation for G(x) given the transformations described?

• F(x + 2) + 3

• F(x - 2) + 3

• F(x - 2) - 3

• F(x + 2) - 3

Why can options B and D be eliminated when determining the equation for G(x)?

• They involve a vertical shift up

• They involve no shift at all

• They involve a horizontal shift left

• They involve a vertical shift down

What is the effect of subtracting a constant from F(x) in terms of vertical translation?

• The graph shifts up

• The graph shifts down

• The graph remains unchanged

• The graph reflects over the y-axis

How can the graphing calculator be used to verify the solution?

• By finding the area under the curve

• By calculating the derivative

• By solving the equation for x

• By checking if the graph matches the given graph

What should be entered into the graphing calculator to verify the transformation?

• The original function F(x)

• The transformed function G(x)

• Both the original and transformed functions

• Only the constant term

What is the purpose of pressing 'Zoom six' on the graphing calculator?

• To clear all functions

• To solve the equation

• To enter a new function

• To set the standard window