Overview
This lecture introduces function notation, how to interpret it, and how to convert between ordered pairs, tables, and graphs using this notation.
Function Notation Basics
- A function relates each input to exactly one output, which is written as f(input) = output.
- Function notation uses f(x), where f is the function name, x is the input, and f(x) is the output.
- You can use function names other than f, such as V or B, depending on the context.
Interpreting Function Notation
- In f(x) = y, x is the input and y is the output; f names the function.
- Example: V(m) = value of an investment (in thousands) after m months.
Examples and Conversions
- V(36) = 17.4 means after 36 months, the investment is worth $17,400 (since 17.4 is in thousands).
- Ordered pair (a, b) corresponds to function notation f(a) = b.
- Example: (-4, 6) is written as f(-4) = 6; f(5) = -1 is written as (5, -1).
Using Tables with Function Notation
- Inputs are listed in the first row (or column), outputs in the second.
- To find B(12), locate 12 in the input row; its output is 50, so B(12) = 50.
- If B(t) = 18, find t where the output is 18 in the table; here, t = 31.
Using Graphs with Function Notation
- Inputs (x-values) are on the horizontal axis, outputs (f(x)-values) are on the vertical axis.
- To find G(2), locate x = 2; if the corresponding y-value is 3, then G(2) = 3.
- To find input given an output, locate the output on the vertical axis, then find the corresponding input.
Key Terms & Definitions
- Function — A rule that assigns each input exactly one output.
- Function Notation — A way to write functions using f(x) to denote output for input x.
- Input — The independent variable, often x, put into the function.
- Output — The dependent variable, result of the function, f(x).
- Ordered Pair — (a, b) where a is the input and b is the output.
Action Items / Next Steps
- Practice writing ordered pairs in function notation and vice versa.
- Complete homework problems converting between tables, graphs, and function notation.