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STANDARDS

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US-SC

Math

South Carolina Math

Pre-Calculus: Building Functions

PC.FBF.1

Write a function that describes a relationship between two quantities.

PC.FBF.1b

Fully covered
Combine 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.3

Fully covered
Describe 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.4

Understand 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.4a

Fully covered
Use composition to verify one function is an inverse of another.

PC.FBF.4b

Fully covered
If a function has an inverse, find values of the inverse function from a graph or table.

PC.FBF.5

Partially covered
Understand 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.