Grade 8 Functions: Input-Output Tables

Complete and analyze function tables

What You'll Learn

Use a rule or a table to find an output or an input
Find a rule’s rate of change and starting value from a table

📖Tables

A function gives each input exactly one output. In y = 3x + 2, the input x = 4 gives the output 3 × 4 + 2 = 14. In a table, the change in y for each step of 1 in x is the rate of change.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
A linear function has these values: when x = 0, 1, 2, 3, y = 11, 3, −5, −13. What is y when x = 7?
1. At x = 0, y = 11, so the y-intercept is b = 11.
2. Each time x goes up by 1, y changes by 3 − 11 = −8, so the rate of change is −8.
3. So the rule is y = −8x + 11.
4. At x = 7: y = −8 × 7 + 11 = −56 + 11 = −45.
5. So y = −45 when x = 7.
Answer: −45
Example 2
For the linear function y = −6x + 10, what value of x makes y = −38?
1. Set the rule equal to −38: −6x + 10 = −38.
2. Undo the + 10: −6x = −38 − 10 = −48.
3. Divide both sides by −6: x = −48 ÷ (−6) = 8.
4. Check: −6 × 8 + 10 = −38.
5. So x = 8.
Answer: 8
Example 3
This table shows a linear function: when x = 3, 6, 9, 12, y = −9, −15, −21, −27. What is the rate of change (slope)?
1. Slope = change in y ÷ change in x (rise over run).
2. When x goes up by 3 (3 to 6), y changes by −15 − (−9) = −6, so the rate of change is −6 ÷ 3 = −2.
3. Every pair of neighboring rows changes at the same rate, so the function is linear.
4. So the rate of change (slope) is −2.
Answer: −2