Building Functions

PC.FBF.1Write a function that describes a relationship between two quantities.PC.FBF.1bCombine functions using the operations addition, subtraction, multiplication, and division to build new functions that describe the relationship between two quantities in mathematical and real-world situations.PC.FBF.3Describe the effect of the transformations kf(x), f(x)+k, f(x+k), and combinations of such transformations on the graph of y=f(x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph.PC.FBF.4Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x)=y and g(y)=x, for all values of x in the domain of f and all values of y in the domain of g, and find inverse functions for one-to-one function or by restricting the domain.PC.FBF.4aUse composition to verify one function is an inverse of another.PC.FBF.4bIf a function has an inverse, find values of the inverse function from a graph or table.PC.FBF.5Understand and verify through function composition that exponential and logarithmic functions are inverses of each other and use this relationship to solve problems involving logarithms and exponents.
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