Common Core Standards: Math
1. Write a function that describes a relationship between two quantities.
A good way to get your students hooked on functions (rather than phonics) is to convince them that functions are all about relationships. For instance, you could say that functions describe their relationships with their parents, their friends, and even celebrities. The glitz and glam of fame should get the attention of at least a few of them.
Students should be able to use functions describe relationships between two quantities, usually x and f(x), where f(x) is some output value that depends on the input value x. Within a particular context, students should be able to express a given relationship as a function.
Unfortunately, they might be more interested in their relationships to Justin Bieber or Megan Fox (which, by the way, are as real as the square root of -1).
- Determine an explicit expression, a recursive process, or steps for calculation from a context.
- Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
- Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.