Transformations of Functions

This video tutorial explains how changes in function equations affect the graph of the function. It covers vertical and horizontal translations, as well as vertical and horizontal stretches and compressions. The video provides examples to illustrate these transformations, helping viewers understand how to recognize and describe the effects of parameter changes on function graphs.

What happens to the graph of a function when a constant is added to the function value?

• The graph compresses horizontally.

• The graph stretches vertically.

• The graph shifts horizontally.

• The graph shifts vertically.

What type of transformation is represented by f(x) - 4?

• Vertical shift up

• Vertical shift down

• Horizontal shift left

• Horizontal shift right

If a constant is added inside the function argument, what type of transformation occurs?

• Vertical stretch

• Horizontal compression

• Horizontal translation

• Vertical translation

If f(x) is transformed to f(x + 4), what happens to the graph?

• Shift 4 units down

• Shift 4 units up

• Shift 4 units right

• Shift 4 units left

What is the effect of multiplying the function value by a negative constant?

• Reflection over the x-axis

• Horizontal stretch

• Vertical compression

• Reflection over the y-axis

When the absolute value of a constant is greater than 1, what type of vertical transformation occurs?

• Horizontal stretch

• Horizontal compression

• Vertical stretch

• Vertical compression

How does the graph of f(x) change when f(x) is multiplied by 0.5?

• Horizontal stretch

• Vertical stretch

• Horizontal compression

• Vertical compression

What is the result of the transformation 3 * f(x)?

• Vertical compression by a factor of 3

• Horizontal stretch by a factor of 3

• Vertical stretch by a factor of 3

• Horizontal compression by a factor of 3

What type of transformation is represented by -f(x)?

• Horizontal stretch

• Reflection over the x-axis

• Reflection over the y-axis

• Vertical stretch

What is the result of the transformation 0.5 * f(x)?

• Horizontal compression by a factor of 0.5

• Vertical compression by a factor of 0.5

• Vertical stretch by a factor of 0.5

• Horizontal stretch by a factor of 0.5