Function Transformations and Graphing

This video tutorial covers function transformations, focusing on horizontal and vertical shifts. It explains how the parameters C and D affect the graph of a function, with C causing horizontal shifts and D causing vertical shifts. The video provides examples and animations to illustrate these concepts, including graphing exercises with absolute value and quadratic functions.

What is the primary focus of the video on function transformations?

• Graphing functions using reflections

• Graphing functions using horizontal and vertical shifts

• Graphing functions using rotations

• Graphing functions using scaling

If you add a constant to the input of a function, in which direction does the graph shift?

• Upward

• Downward

• Left

• Right

What happens to the graph of a function when you subtract a constant from the input?

• It shifts upward

• It shifts downward

• It shifts to the right

• It shifts to the left

How does adding a constant to the output of a function affect its graph?

• Shifts the graph to the right

• Shifts the graph upward

• Shifts the graph to the left

• Shifts the graph downward

What is the effect of subtracting a constant from the output of a function?

• The graph shifts downward

• The graph shifts to the left

• The graph shifts to the right

• The graph shifts upward

In the example of graphing the absolute value function, what is the first step?

• Apply horizontal shifts

• Draw the final graph

• Identify the parent function

• Apply vertical shifts

How does the graph of the absolute value function change when you add 3 to the input?

• Shifts up 3 units

• Shifts left 3 units

• Shifts down 3 units

• Shifts right 3 units

What is the parent function for the quadratic function example?

• y = |x|

• y = x^3

• y = x^2

• y = x

In the quadratic function example, what does subtracting 2 from the input do to the graph?

• Shifts it down 2 units

• Shifts it up 2 units

• Shifts it right 2 units

• Shifts it left 2 units

What is the final step in graphing the quadratic function using transformations?

• Identify the parent function

• Apply horizontal shifts

• Apply vertical shifts

• Draw the final graph