Understanding Function Transformations

The video tutorial explains how to transform the function F(x) = √x into G(x) by shifting it down two units and right three units. It details how the values of C and D affect the graph's position, with C shifting the graph horizontally and D vertically. The tutorial uses animations to illustrate these transformations and provides the formula for G(x) in terms of F(x). It concludes with a summary of the transformation rules for shifting graphs.

What is the initial function given in the problem?

• f(x) = x^3

• f(x) = 1/x

• f(x) = √x

• f(x) = x^2

What transformation is applied to f(x) to form g(x)?

• Shift down three units and right two units

• Shift down two units and right three units

• Shift up two units and left three units

• Shift up three units and left two units

In the formula g(x) = f(x + C) + D, what does the value of D represent?

• Horizontal shift

• Vertical shift

• Reflection

• Stretching

If D is negative, in which direction is the graph shifted?

• Left

• Up

• Right

• Down

What happens to the graph when C is positive?

• It shifts down

• It shifts right

• It shifts left

• It shifts up

For a shift of right three units, what should be the value of C?

• C = 3

• C = -3

• C = 2

• C = -2

What is the final expression for g(x) in terms of f(x)?

• g(x) = f(x - 3) - 2

• g(x) = f(x + 3) + 2

• g(x) = f(x - 2) + 3

• g(x) = f(x + 2) - 3

If the graph is shifted left by C units, what is the sign of C?

• Zero

• Undefined

• Positive

• Negative

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

• Shifts the graph down

• Shifts the graph right

• Shifts the graph left

• Shifts the graph up

How would you express g(x) if f(x) = √x and the graph is shifted right by 3 units and down by 2 units?

• g(x) = √(x - 2) + 3

• g(x) = √(x - 3) - 2

• g(x) = √(x + 3) + 2

• g(x) = √(x + 2) - 3