Overview transformations horizontal shifts - Online Tutor - Free Math Videos

The video tutorial explains horizontal transformations in functions, contrasting them with vertical transformations. It discusses how adding or subtracting a constant inside the function affects the graph's horizontal position. The tutorial provides examples to illustrate these concepts, emphasizing that positive values shift the graph left, while negative values shift it right. The video aims to clarify common misconceptions about the direction of shifts in horizontal transformations.

What happens to the graph of a function when a positive constant is added inside the function's argument?

• The graph shifts upwards.

• The graph shifts downwards.

• The graph shifts to the right.

• The graph shifts to the left.

In the context of horizontal transformations, what is a common mistake when interpreting a positive shift?

• Assuming the graph shifts to the right.

• Assuming the graph shifts downwards.

• Assuming the graph shifts to the left.

• Assuming the graph shifts upwards.

When dealing with the function f(x) = √(x + 3), what is the correct direction of the shift?

• Shift down by 3 units.

• Shift right by 3 units.

• Shift left by 3 units.

• Shift up by 3 units.

If a function is transformed by f(x) = √(x - 1), what is the direction of the shift?

• Shift down by 1 unit.

• Shift up by 1 unit.

• Shift left by 1 unit.

• Shift right by 1 unit.

What is the new position of the point (2, 4) on the graph of f(x) = x^2 when transformed by f(x) = (x - 1)^2?

• (3, 4)

• (1, 4)

• (1, 1)

• (2, 1)

How does the graph of f(x) = x^2 change when transformed to f(x) = (x + 1)^2?

• It shifts left by 1 unit.

• It shifts down by 1 unit.

• It shifts right by 1 unit.

• It shifts up by 1 unit.

What is a key takeaway about horizontal transformations when the constant is inside the function?

• The graph always shifts downwards.

• The shift direction is opposite to the sign of the constant.

• The graph always shifts upwards.

• The shift direction is the same as the sign of the constant.