F-BF: Building Functions

Building Functions

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Building Functions covers constructing new functions from contexts, combining existing functions, and working with inverses. Explicit rules, recursive processes, and transformations such as translations and reflections all appear. Arithmetic and geometric sequences serve as entry points for connecting recursive and explicit representations.

F-BF.1Write a function that describes a relationship between two quantities.F-BF.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.F-BF.3Identify 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.4Find inverse functions.F-BF.5(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Example Problems
Integrate:
Find the sum:
Is the following function even, odd, or neither?
is a finite function whose domain is the letters a to e. The following table lists the output for each input in 's domain.

xabcde
4545302520


Is
invertible?
Evaluate:
Goblins

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