- Understand what a function is and use the vertical line test to check if a graph shows a function
- Use function notation [latex]f(x)[/latex] and evaluate functions
- Recognize the graphs of common functions
Streaming Service Example
Imagine you work for a streaming service that analyzes user behavior. Today you’re examining how the number of hours people spend watching shows relates to their monthly subscription cost.
Your streaming service offers different subscription tiers based on viewing hours:
- Basic Plan: Up to 20 hours for $8.99/month
- Standard Plan: Up to 50 hours for $13.99/month
- Premium Plan: Unlimited hours for $18.99/month
You’ve collected data from 6 users showing their viewing hours and monthly costs:
| User | Hours Watched | Monthly Cost |
|---|---|---|
| Alex | 15 | $8.99 |
| Jordan | 45 | $13.99 |
| Sam | 25 | $13.99 |
| Casey | 75 | $18.99 |
| Taylor | 30 | $13.99 |
| Morgan | 60 | $18.99 |
Since cost is a function of hours watched, we can write this relationship using function notation.
If we have a function where the output depends on the input, we write:
[latex]f(\text{input})=\text{output}[/latex]
This is read as “f of input equals output” or “output is a function of input”
Let’s call our function C (for Cost), so: C(h) = monthly cost when h hours are watched
- Domain: All possible input values
- Range: All possible output values