Question

lesson practice
a1.4.01
name date period

1. rule a takes any word as an input

and writes the word backwards as
an output.
is rule a a function?
explain your thinking
rule a
input hat sock racecar
output tah kcos racecar
problems 2–3: here is rule b.

1. is rule b a function?

explain your thinking.
rule b
input 4 6 6 5
output blue purple yellow white

1. predict what the output could be when the input is 3.

problems 4–5: here is rule c.

1. is rule c a function?

explain your thinking.
rule c
input 6 8 12 14
output 4 6 10?

1. predict the missing output for rule c.
2. this table shows the total number of days in each month of a given year.

jan feb mar apr may jun jul aug sep oct nov dec
28 ×
29 ×
30 × × × ×
31 × × × × × × × ×
imagine a rule where the input is a month and the output is the number of days in
that month. does this rule represent a function? explain your thinking.
unit 4 lesson 1
363

Explanation:

Problem 1

Step1: Recall function definition

A function is a relation where each input has exactly one output.

Step2: Analyze Rule A

For Rule A, each input word (hat, sock, racecar) has exactly one output (the word reversed: tah, kcos, racecar). No input has more than one output.

Step1: Recall function definition

A function requires each input to have exactly one output.

Step2: Analyze Rule B

In Rule B, the input \( 6 \) has two outputs: purple and yellow. Since an input has more than one output, it violates the function definition.

Step1: Note Rule B's nature

Since Rule B is not a function (input \( 6 \) has multiple outputs), for input \( 3 \), there's no fixed rule, but we can pick a color (e.g., red, green, etc.) as output.

Step2: Choose a possible output

We can choose any color, say "red" (or any other color like "green", "orange", etc.).

Answer:

Yes, Rule A is a function. Because every input word has exactly one output (the word written backwards), satisfying the definition of a function (each input has exactly one output).

Problem 2