5.A.3: My definition of Equations and Functions
November 5, 2009Equation: A number sentence that contains numbers and/or a variable, an operation and an equal sign, such that the value(s) for the variable (if there is one) can be determined. Equations may be linear (straight line) or nonlinear (polynomial equations of the 2nd degree and up). Equations are “solved.”
Examples include:
Ex. 1: Ex. 2:
2 + x = 9 x2 = 4
-2 + 2 + x = 9 + -2 √x2 = √4
x = 7 x = 2 AND x = -2
Function: An equation, where for each value of x (input) there is one and only one y (output). Functions are usually notated as f(x) [read verbally as “f of x”]. Functions can be linear and nonlinear. Functions have domains (the input values for x) and ranges (the resulting output value or y).
Examples include:
f(x) = x + 2
| x | x + 2 |
| 1 | 3 |
| 2 | 4 |
| 3 | 5 |
f(x) = x2
| x | x2 |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
There are several activities that I would use to reinforce the concepts of functions, equations, variables, and linear patterns/equations.
1. Compare & contrast, using a Venn diagram, functions and equations (this could also be done as a journal enty).
2. Journal entry: Solve for x a given equation, e.g. x + 2 = 7. Solve for x + 2 = 9. Equals 10. Equals 12. Describe what happens when the sum changes. How would you define x? Why?
3. The function machine applet set up on a SmartBoard as a math activity.
4. Journal entry: Explain why “x2 = 4” is an equation and “f(x) = x2” is a function?
5. For given table(s), write a formula that defines the relationship between each of the values.
6. “Guess My Rule” calculator game in groups of four.
7. Webquest, done in groups of four, on Fibonacci Numbers, Golden Ratio, and Fractals with outcome a formal presentation to the class on results of the webquest.
