Topic: Building Functions |
Common Core Mathematics 9-12 |
| Cluster Build a function that models a relationship between two quantities |
| | Grade 9-12 |
| | | F.BF.1. | Write a function that describes a relationship between two quantities. |
| | | F.BF.1.a. | Determine an explicit expression, a recursive process, or steps for
calculation from a context. |
| | | F.BF.1.b. | 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. |
| | | F.BF.1.c. | (+) 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. |
| | | F.BF.2. | Write arithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and translate
between the two forms. |
| Cluster Build new functions from existing functions |
| | Grade 9-12 |
| | | F.BF.3. | Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and
illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. |
| | | F.BF.4. | Find inverse functions. |
| | | F.BF.4.a. | Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For
example, f(x)=2 x^{3} or f(x) = (x+1)/(x-1) for x≠ 1. |
| | | F.BF.4.b. | (+) Verify by composition that one function is the inverse of
another. |
| | | F.BF.4.c. | (+) Read values of an inverse function from a graph or a table,
given that the function has an inverse. |
| | | F.BF.4.d. | (+) Produce an invertible function from a non-invertible function
by restricting the domain. |
| | | F.BF.5. | (+) Understand the inverse relationship between exponents and
logarithms and use this relationship to solve problems involving
logarithms and exponents. |