Give Me Five

Learning Focus

Move among five representations of a function: words, table, graph, equation, and context.

Big idea

The same relationship can be shown five ways:

1. Words / story
2. Table of values
3. Graph
4. Equation
5. Context (units and meaning)

Linear: constant difference in $y$ for equal steps in $x$. Exponential: constant ratio.

Build any representation from another by finding the start value and the rate (or ratio).

Worked example

Table: $x=0,1,2,3$ and $y=4,7,10,13$.

• Differences are all $3$: linear.
• Start value $4$, rate $3$: $y=3x+4$.
• Words: "start at 4 and add 3 each step."
• Graph: line with $y$-intercept $4$ and slope $3$.
• $x=10$: $y=34$.

Takeaways

• Each representation should tell the same story.
• Check differences (linear) or ratios (exponential) in a table.
• Identify start value and rate to write an equation.