Sept. 14 Class

Learning Goals

• Understand how reflections transform a function.
• Understand how horizontal stretches transform a function.

Congratulations on completing your formative quizzes today!

After we quiz we discussed reflections and how they work.  If the parent function is y = f(x), then

y = -f(x) is a reflection in the x-axis.

y = f(-x) is a reflection in the y-axis.

I then worked out solutions to this worksheet:

Handout: Reflections 

Examples

A reflection in the x-axis.

A reflection in the y-axis.

Next we talked about horizontal stretches.  If the parent function is y = f(x), then the horizontally stretched function is given by,

y = f(kx)

By working out an explicit example we found that if the function is transformed with a k, the function stretches by a factor of 1/k.

Example

The original function is in black and the transformed function is in red.

In the above example, the value of k is 2.  Therefore the graph is "stretched" by a factor of 1/2.

(This can also be referred to as a compression by a factor of 2)

A reflection in the y-axis of the above example would look like this:

The reflected function is shown in blue.

Homework: All from the following handouts, 

Horizontal Stretches (Ignore vertical stretches pages.)

Functions Workshop (Parts I - VI)