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5.8: What's My Rule

Difficulty Level: At Grade Created by: CK-12

What's My Rule? - Write Rules For One-Step Function Tables

Students identify relationships between the input and output in two-column tables, and write rules that describe the relationship. Rules may be written in words or symbols or both ways. All functions involve one computational step, addition, subtraction, multiplication, or division.

Solutions

1.

\begin{align*}u\end{align*}u \begin{align*}v\end{align*}v
7 9
4 6
1 3
0 2
1. 2 4
2. 9 11
3. 3 5
4. 8 10
5 Rule: \begin{align*}v=u+2\end{align*}v=u+2

2.

\begin{align*}w\end{align*}w \begin{align*}y\end{align*}y
10 6
15 11
13 9
5 1
1. 8 4
2. 14 10
3. 7 3
4. 16 12
5 Rule: \begin{align*}y=w-4\end{align*}y=w4

3.

\begin{align*}z\end{align*}z \begin{align*}a\end{align*}a
7 37
10 40
18 48
45 75
1. 31 61
2. 14 44
3. 8 38
4. 29 59
5 Rule: \begin{align*}a=z+30\end{align*}a=z+30

4.

\begin{align*}b\end{align*}b \begin{align*}c\end{align*}c
48 28
50 30
28 8
42 22
1. 67 47
2. 59 39
3. 75 55
4. 34 14
5 Rule: \begin{align*}c=b-20\end{align*}c=b20

5.

\begin{align*}d\end{align*}d \begin{align*}e\end{align*}e
3 12
8 32
2 8
5 20
1. 1 4
2. 7 28
3. 6 24
4. 9 54
5 Rule: \begin{align*}e=4 \times d\end{align*}e=4×d

6.

\begin{align*}f\end{align*}f \begin{align*}g\end{align*}g
10 2
40 8
25 5
5 1
1. 15 3
2. 35 7
3. 20 4
4. 45 9
5 Rule: \begin{align*}g=f \div 5\end{align*}g=f÷5

7.

\begin{align*}h\end{align*} \begin{align*}j\end{align*}
2 18
5 45
7 63
1 9
1. 4 36
2. 3 27
3. 6 54
4. 9 81
5 Rule: \begin{align*}j=9 \times h\end{align*}

8.

\begin{align*}k\end{align*} \begin{align*}m\end{align*}
21 7
18 6
6 2
27 9
1. 9 3
2. 24 8
3. 12 4
4. 30 10
5 Rule: \begin{align*}m=k \div 3\end{align*}

\begin{align*}p\end{align*} and \begin{align*}t\end{align*} stand for numbers.

Write the rule. Complete the table.

\begin{align*}& \mathbf{Describe} && \text{I see a table with two columns}.\\ &&& p \ \text{and} \ t \ \text{stand for numbers}.\\ & \mathbf{My \ Job} && \text{Figure out the rule}.\\ &&& \text{What do I have to do to} \ p \ \text{to get} \ t?\\ &&& \text{Then complete rows} \ 1, 2, 3 \ \text{and} \ 4.\\ & \mathbf{Plan} && \text{I can add, subtract, mulitply or divide. I have to use the same operation on}\\ &&& \text{all} \ p \ \text{numbers to get the} \ t \ \text{numbers}.\\ & \mathbf{Solve} && \text{All} \ t \ \text{numbers are} \ 3 \ \text{times} \ p \ \text{numbers}.\\ &&& \text{The rule is multiply} \ p \ \text{by} \ 3 \ \text{to get} \ t. \ \text{I can write} \ t = 3 \times p\\ & \mathbf{Check}\end{align*}

Write the rule. Complete the table.

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CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.5.8

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