Exploring Function Transformations

The video tutorial explains how to transform functions by altering their shape, size, or direction. It covers vertical and horizontal shifts, reflections over the x and y axes, and vertical and horizontal stretches and compressions. The tutorial also discusses the order of applying these transformations and provides examples to illustrate the concepts. Key points include understanding how changes affect the range and domain of functions.

What happens to the graph of f(x) when you add a positive constant T to it?

• It shifts to the left.

• It shifts up.

• It shifts down.

• It shifts to the right.

How does the graph of f(x) change when you subtract a constant C inside the parentheses?

• It shifts to the left.

• It shifts to the right.

• It shifts up.

• It shifts down.

What is the effect of a negative sign outside the function f(x)?

• It shifts the graph down.

• It shifts the graph up.

• It reflects the graph over the x-axis.

• It reflects the graph over the y-axis.

What does f(-x) do to the graph of f(x)?

• Shifts it down.

• Shifts it up.

• Reflects it over the y-axis.

• Reflects it over the x-axis.

What happens to the graph of f(x) when it is multiplied by a number greater than 1?

• It shifts to the left.

• It undergoes a vertical compression.

• It shifts to the right.

• It undergoes a vertical stretch.

If f(x) is multiplied by a number between 0 and 1, what transformation occurs?

• Horizontal compression

• Vertical stretch

• Vertical compression

• Horizontal stretch

What is the effect of multiplying x by a number greater than 1 in f(bx)?

• Vertical compression

• Horizontal stretch

• Vertical stretch

• Horizontal compression

How do you achieve a horizontal compression by a factor of 1/2?

• Multiply y-values by 2.

• Divide x-values by 2.

• Multiply x-values by 2.

• Divide y-values by 2.

In what order should multiple transformations be applied?

• Horizontal translation, stretching/shrinking, reflecting, vertical translation

• Reflecting, horizontal translation, vertical translation, stretching/shrinking

• Stretching/shrinking, reflecting, horizontal translation, vertical translation

• Vertical translation, reflecting, stretching/shrinking, horizontal translation

What happens to the y-values when you reflect a graph over the x-axis?

• They remain the same.

• They double.

• They change signs.

• They halve.