P.F.BF.A: Build new functions from existing functions.

Build new functions from existing functions.

P.F.BF.A.1Understand how the algebraic properties of an equation transform the geometric properties of its graph (for example, given a function, describe the transformation of the graph resulting from the manipulation of the algebraic properties of the equation such as translations, stretches, reflections, and changes in periodicity and amplitude).P.F.BF.A.2Develop an understanding of functions as elements that can be operated upon to get new functions: addition, subtraction, multiplication, division, and composition of functions.P.F.BF.A.3Compose 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).P.F.BF.A.4Construct the difference quotient for a given function and simplify the resulting expression.P.F.BF.A.5Find inverse functions (including exponential, logarithmic, and trigonometric).P.F.BF.A.6Explain why the graph of a function and its inverse are reflections of one another over the line y = x.
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