119 Powerpoint 2.2

2.2 Functions ,[object Object],[object Object],[object Object],[object Object],[object Object]

A. Different ways relations can look: ,[object Object],[object Object],[object Object],[object Object]

A FUNCTION, however, is ,[object Object],[object Object]

{(4,2), (2,1), (3,2), (1,4)} is a function ,[object Object],[object Object],[object Object]

Vertical Line Test ,[object Object]

B. “f(x)” is read “f of x” ,[object Object],[object Object]

C. If f(x) = 3 – 2x, then find f(-1) ,[object Object]

Try: Find f(-1/2) for f(x) = 3 - 2x

Let g(x)=-x 2 +4x+1. Find g(x+2). ,[object Object]

Try: h(t) = t 2 – 2t. Find h(x + 2).

A piecewise function looks like: ,[object Object],[object Object],[object Object],[object Object]

For that last piecewise f’n, ,[object Object],[object Object],[object Object]

Try: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Here are a few problems where the instructions are important. ,[object Object],[object Object],[object Object],[object Object]

You try: “Find all the real values of x such that f(x) = 0.” ,[object Object]

Another set of interesting instructions: ,[object Object],[object Object],[object Object]

You try: Find all values of x for which f(x)=g(x) if f(x)=x 2 +2x+1 and g(x)=3x+3.

E. This is called a difference quotient: It’s a special formula you will derive in your calculus class. You will not have to memorize this formula for your algebra exams. It will be provided to you if we want you to use it on the test. Why are we looking at it before you are in calculus? Getting from this formula to an answer will be all algebra-esque, lots of distributing, combining like terms, etc.

Find and simplify the difference quotient if f(x) = x 2 – x + 1 ,[object Object],[object Object],[object Object],[object Object],[object Object]

This time, x will be replaced with the number 2. f(x) = x 2 – x + 1 ,[object Object]

119 Powerpoint 2.2

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119 Powerpoint 2.2