Graph Shifts and Transformations

The video tutorial explains how adding or subtracting values to the input of a function affects the graph's position. Adding a value shifts the graph to the left, while subtracting shifts it to the right. The tutorial uses specific points on the graph to demonstrate these shifts, concluding with a verification of the graph's new position.

What is the main focus of the problem discussed in the video?

• Determining the graph line when f(x^2) is replaced by f(x + 2)

• Finding the derivative of f(x^2)

• Solving for x in the equation f(x^2) = 0

• Calculating the area under the curve of f(x^2)

What happens to the graph of a function when you add a number to the input?

• It moves downwards

• It moves upwards

• It shifts to the left

• It shifts to the right

If f(x - 2) is applied to a graph, in which direction does the graph shift?

• Right by two units

• Up by two units

• Down by two units

• Left by two units

How does f(x + 2) affect the graph of f(x^2)?

• Moves it downwards by two units

• Shifts it to the right by two units

• Shifts it to the left by two units

• Moves it upwards by two units

Which line does the point (0, 0) shift to when f(x + 2) is applied?

• Green line

• Yellow line

• Blue line

• Red line

What is the new position of the point (-1, 1) after applying f(x + 2)?

• (-3, 1)

• (-1, 3)

• (-3, -1)

• (-1, -1)

Which line represents the graph of f(x + 2) after the shift?

• Blue line

• Green line

• Red line

• Yellow line

How can you verify the shift of the graph using input values?

• By calculating the area under the curve

• By comparing the outputs of f(x) and f(x + 2)

• By finding the intersection points with the axes

• By checking the slope of the line

What is the output when the input is 0 for f(x + 2)?

• (0, 2)

• (0, 0)

• (0, -2)

• (0, 4)

What does the shift of f(x + 2) indicate about the graph's movement?

• It moves to the right

• It moves downwards

• It moves to the left

• It moves upwards