Master How to identify the transformations from a family of functions

The video tutorial explains how to apply transformations to functions, using an arbitrary function F(x) as an example. It covers the concept of parent functions, vertical and horizontal shifts, reflections, and stretches. The tutorial provides detailed examples to illustrate how these transformations affect the graph of a function.

What is the term used for the original form of a function before any transformations?

• Base function

• Parent function

• Core function

• Root function

How does adding a positive number outside a function affect its graph?

• Shifts it to the left

• Shifts it to the right

• Shifts it downwards

• Shifts it upwards

What type of shift occurs when a number is added inside the function?

• Vertical shift

• Horizontal shift

• Diagonal shift

• No shift

What happens to a function's graph when it is multiplied by a negative number outside the function?

• It shifts upwards

• It reflects over the x-axis

• It shifts downwards

• It reflects over the y-axis

If a function is multiplied by a negative number inside the parentheses, what transformation occurs?

• Reflection over the x-axis

• Vertical stretch

• Horizontal compression

• Reflection over the y-axis

What is the effect of multiplying a function by a number greater than one?

• Vertical stretch

• Horizontal compression

• Vertical compression

• Horizontal stretch

How does multiplying a function by a number less than one affect its graph?

• Vertical stretch

• Horizontal stretch

• Horizontal compression

• Vertical compression

In the example of a function with a negative sign inside the parentheses, what transformation is illustrated?

• Reflection over the x-axis

• Reflection over the y-axis

• Horizontal compression

• Vertical stretch

What transformation occurs when a function is shifted left by adding a positive number inside the function?

• Shift down

• Shift up

• Shift left

• Shift right

In the examples provided, what is the result of adding a number outside the function?

• Horizontal shift

• Vertical shift

• Reflection

• No change