Thursday 27 February class

Topics:

• Reminders about the relationship between the square root and squaring.

• Composition of functions: Definition 6.5 p. 77. Start here!

• Finding the formula of a composite function

• Using functions defined by tables

• The square root principle (see this post) vs. the definition of square root: what is ? (Came up in Example 6.8(c)) – see fuller discussion below

• One-to-one functions

• The horizontal line test for one-to-one functions

The square root principle and related things:

The square root principle (as it is sometimes called) says that

if

then .

This is related to two other facts connecting squaring and square roots:

• — This is the definition of the square root of x. ( is the number which, when squared, gives you x.)

• — This is because the radical sign indicates that you should take the non-negative square root, so  is always greater than or equal to 0 no matter what x is.

Many people get the bad idea in their heads that  is the same as x. That is not true as a general rule. It is only true when . Be careful!

Homework:

• Reread/ review the examples. Make sure that you understand how composition works: we go through first one, then the other, of the functions.

• Do the assigned parts of Exercises 6.3, 6.4, 6.5, and 7.1

• Do the WeBWorK: start early! post questions to Piazza!

• Do the Warm-Up   (due by Monday night 11 PM also)