Building Functions

F.BF.1Use functions to model real-world relationships.F.BF.1a(9/10) Combine multiple functions to model complex relationships. For example, p(x) = r(x) - c(x); (profit = revenue - cost).F.BF.1b(11) Determine an explicit expression, a recursive function, or steps for calculation from a context.F.BF.1c(11) 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 and series both recursively and with an explicit formula, use them to model situations, and translate between the two forms.F.BF.3(9/10/11) Transform parent functions (f(x)) by replacing f(x) with f(x) + k, kf(x), f(kx), adn 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. For (9/10) focus on linear, quadratic, and absolute value functions.F.BF.4Find inverse functions.F.BF.4a(11) Write an expression for the inverse of a function.F.BF.4b(11) Read values of an inverse function from a graph or a table, given that the function has an inverse.F.BF.4c(+) Verify by composition that one function is the inverse of another.F.BF.4d(+) Produce an invertible function from a non-invertible function by restricting the domain.F.BF.5(11) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
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