Thursday 20 February class

Topics:

• 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 \sqrt{x^2}? (Came up in Example 6.8(c)) – see fuller discussion below

 

 

The square root principle and related things:

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

if x^2 = c

then x = \pm\sqrt{c}.

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

(\sqrt{x})^2 = x — This is the definition of the square root of x. (\sqrt{x} is the number which, when squared, gives you x.)

\sqrt{x^2} = |x| — This is because the radical sign indicates that you should take the non-negative square root, so \sqrt{x^2} is always greater than or equal to 0 no matter what x is.

 

Many people get the bad idea in their heads that \sqrt{x^2} is the same as x. That is not true as a general rule. It is only true when x\ge 0. 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.

• See the homework from last time – especially #5.3 (needed for Test 1!)

• Do the assigned problems from Session 6, but omit 6.1 and 6.2

• No new WeBWorK or Warm-Up today, but I have extended one WeBWorK until tonight 11 PM so if you got cut off you can do it (no further extensions!!!) and the Warm-Up on Piazza is open until the night after Test 1.

 

Test 1 Review

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