Understanding Function Transformations

The video tutorial explains how to derive equations for functions A, B, C, and D by applying transformations to the basic square root function. It covers flipping over axes, shifting, and changing signs under the radical. The tutorial provides step-by-step instructions for each function, emphasizing the effects of these transformations on the function's graph and domain.

What is the initial observation about the functions A, B, C, and D?

• They resemble y = x^3.

• They resemble y = √x.

• They resemble y = x^2.

• They resemble y = 1/x.

How do you flip a function over the horizontal axis?

• Subtract a constant from the function.

• Add a constant to the function.

• Divide the function by -1.

• Multiply the function by -1.

What transformation is applied to derive function A from the flipped function?

• Shift left by 3 and up by 1.

• Shift right by 3 and down by 1.

• Shift right by 1 and down by 3.

• Shift left by 1 and up by 3.

What is the domain of function B?

• x is less than or equal to 3.

• x is greater than or equal to -3.

• x is greater than or equal to 3.

• x is less than or equal to -3.

How is function B derived from function A?

• By dividing the radical by a constant.

• By multiplying the radical by a constant.

• By flipping the sign of everything under the radical.

• By adding a constant to the radical.

What is the shift applied to derive function D from the original function?

• Shift down by 3 and right by 1.

• Shift down by 1 and right by 3.

• Shift up by 1 and left by 3.

• Shift up by 3 and left by 1.

How is function C different from function D?

• Function C has the sign under the radical flipped.

• Function C is shifted up by 1 and left by 3.

• Function C is multiplied by a constant.

• Function C is shifted down by 1 and right by 3.

What happens when you increase the value inside the radical?

• The graph shifts to the left.

• The graph shifts up.

• The graph shifts to the right.

• The graph shifts down.

What is the effect of making the value inside the radical smaller or negative?

• The graph shifts down.

• The graph shifts up.

• The graph shifts to the right.

• The graph shifts to the left.

What must be true for the starting point of the function?

• The value under the radical must be one.

• The value under the radical must be positive.

• The value under the radical must be negative.

• The value under the radical must be zero.