Understanding Graph Transformations

The video tutorial explains how to transform the function f(x) = x^2 by shifting it up four units and left one unit to create a new function G(x). It details the role of parameters C and D in shifting graphs horizontally and vertically. An animation demonstrates these transformations, and the tutorial concludes with a summary of how to express G(x) in terms of f(x) and the effects of positive and negative values of C and D on graph shifts.

What is the initial function f(x) that we are transforming?

• f(x) = 2x

• f(x) = x^2

• f(x) = x^3

• f(x) = x + 2

If C is positive, in which direction is the graph shifted?

• Down

• Left

• Up

• Right

What happens to the graph when D is negative?

• The graph shifts up

• The graph shifts right

• The graph shifts down

• The graph shifts left

How do you shift the graph of f(x) = x^2 up by four units?

• Subtract 4 from x^2

• Add 4 to x^2

• Subtract 4 from x

• Add 4 to x

What is the effect of having x + 1 inside the function?

• Shifts the graph left by one unit

• Shifts the graph right by one unit

• Shifts the graph up by one unit

• Shifts the graph down by one unit

What is the formula for G(x) after shifting f(x) = x^2 up four units and left one unit?

• G(x) = (x - 1)^2 - 4

• G(x) = (x - 1)^2 + 4

• G(x) = (x + 1)^2 - 4

• G(x) = (x + 1)^2 + 4

How can G(x) be expressed in terms of f(x) after the transformations?

• G(x) = f(x - 1) + 4

• G(x) = f(x + 1) + 4

• G(x) = f(x + 1) - 4

• G(x) = f(x - 1) - 4

If C is negative, what is the effect on the graph?

• The graph shifts down

• The graph shifts left

• The graph shifts right

• The graph shifts up

What is the effect of a positive D on the graph?

• The graph shifts down

• The graph shifts up

• The graph shifts right

• The graph shifts left

Which of the following correctly summarizes the transformation rules for C and D?

• C shifts up/down, D shifts up/down

• C shifts up/down, D shifts left/right

• C shifts left/right, D shifts left/right

• C shifts left/right, D shifts up/down