Alignments to Content Standards
- Alignment: F-IF.A.1
- HSF: Functions
- Domain: HSF-IF: Interpreting Functions
- Cluster: Understand the concept of a function and use function notation.
- Standard: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Task
Anthony’s electricity company charges him $0.12 per kWh (kilowatt-hour) of electricity, plus a basic connection charge of $20.00 per month. Let C(k) be the cost in dollars at the end of the month and k be the kilowatt-hour.
- Write the function using C(k) be the cost in dollars and k for the kilowatt-hour.
- Complete the table below.
| k (kilowatt-hour) | C(k) (dollars) |
| 0 | |
| 15 | |
| 35 | |
| 47 | |
| 89 | |
| 125 | |
| 260 |
- Sketch a graph of C for 0≤k≤280.
- What is the domain and range of the function?
- Is C a function of k? Explain you reasoning.
Commentary
The purpose of the task is to illustrate the meaning of a function in a real-world situation. This task is helping the students understand and visualize whether or not this is a function. Students are also getting a sense of what it means for an equation to be a function. While solving this problem students are also answering whether each input only has one output. In future classes students will be able to use their knowledge of functions to be able to derive them.