Week 23: Functions, coin problems, and reading data

Field Book

82 to 85

Due

Test 20 due

Method

Paper first, every step

Function notation is new punctuation, not new mathematics. When you see f(3) it means put 3 wherever x appears and compute. That is all. Coin problems introduce the two-column habit that carries straight into value and motion problems later: how many of a thing, and what each one is worth.

What you have to be able to do

Evaluate a function at a given value and state domain and range
Set up a coin problem with two columns
Read a stem-and-leaf plot and a histogram

The procedures

Evaluating a function

f(x) is just a name for the expression. f(3) means substitute 3 for every x.
Compute carefully, watching signs when the input is negative.
The domain is every input allowed. The range is every output that comes out.

Coin and value problems

Make two columns: how many, and what each one is worth.
Number times value gives total value for each row.
Write two equations: one counting the items, one totaling the money. Then solve as a system.

Reading a stem-and-leaf plot

The stem is the tens digit and each leaf is a ones digit.
Every leaf is one data point, so count leaves to count data.
The plot keeps the actual values, which a histogram does not.

Worked

WORKED

If f(x) = 2x + 5, find f(3).
Substitute 3 for x: 2(3) + 5.
ANSWER: f(3) = 11

WORKED

Twelve coins, nickels and dimes, are worth 95 cents. How many of each?
Count: n + d = 12. Value: 5n + 10d = 95.
Substitute d = 12 − n into the value equation: 5n + 120 − 10n = 95.
−5n = −25, so n = 5.
ANSWER: 5 nickels and 7 dimes

Terms

Term	Meaning
function	a rule that gives exactly one output for each input
domain	the set of allowed inputs
range	the set of outputs the function actually produces

Check yourself

1. If f(x) = 3x − 1, find f(4)

2. If f(x) = x², find f(−3)

3. Ten coins, dimes and quarters, worth $1.60. Which two equations set it up?

reveal answers

11 · 9 · d + q = 10 and 10d + 25q = 160

This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.