Unit 5, Lesson 3
Equations for Functions
Grade 8
3.1
Warm-up
A Square’s Area
Fill in the table of input-output pairs for the given rule. Write an algebraic expression for the rule in the box in the diagram.
| input | output |
|---|---|
| 8 | |
| 2.2 | |
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Fill in the table of input-output pairs for the given rule. Write an algebraic expression for the rule in the box in the diagram.
| input | output |
|---|---|
| 8 | |
| 2.2 | |
Record your answers to these questions in the table provided.
| description | a | b | c | d |
|---|---|---|---|---|
| diagram | ||||
| equation | ||||
| input = 5 output = ? |
||||
| independent variable |
||||
| dependent variable |
We can sometimes represent functions with equations. For example, the area,
We can also draw a diagram to represent this function:
In this case, we think of the radius,
Since
We sometimes get to choose which variable is the independent variable in the equation. For example, if we know that
then we can think of
or we can think of
A dependent variable represents the output of a function.
For example, someone needs to buy 20 pieces of fruit and decides to buy apples and bananas. If they select the number of apples first, the equation
An independent variable represents the input of a function.
For example, suppose someone needs to buy 20 pieces of fruit and decides to buy some apples and bananas. If they select the number of apples first, the equation
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