Identifying Transformations in Function Families

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 graphs and how transformations such as vertical and horizontal shifts, reflections, and stretching affect these graphs. The tutorial provides detailed explanations and examples to illustrate these transformations, ensuring that viewers understand how to apply them to any function.

Which of the following is an example of a function that could be represented by f(x)?

• All of the above

• x^3

• log(x)

• sin(x)

What is a parent graph?

• A graph with only horizontal shifts

• A graph with only vertical shifts

• A graph without any transformations

• A graph with transformations

What happens when you add a positive number outside the function f(x)?

• The graph shifts left

• The graph shifts up

• The graph shifts down

• The graph shifts right

If f(x) is transformed to f(x - h), what type of shift occurs?

• Vertical shift up

• Vertical shift down

• Horizontal shift left

• Horizontal shift right

What does a negative sign inside the function, as in f(-x), indicate?

• Reflection over the y-axis

• Horizontal shift right

• Reflection over the x-axis

• Vertical shift down

What does multiplying the function f(x) by a negative number outside the function indicate?

• Vertical shift up

• Horizontal shift left

• Reflection over the y-axis

• Reflection over the x-axis

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

• Horizontal compression

• Horizontal stretch

• Vertical compression

• Vertical stretch

What happens when the absolute value of a is less than 1 in the transformation a*f(x)?

• Horizontal compression

• Vertical compression

• Horizontal stretch

• Vertical stretch

If f(x) is transformed to f(bx) and the absolute value of b is greater than 1, what type of transformation occurs?

• Vertical stretch

• Horizontal compression

• Vertical compression

• Horizontal stretch

What is the effect of adding a positive number inside the function f(x + h)?

• Vertical shift up

• Vertical shift down

• Horizontal shift left

• Horizontal shift right