A2.F.1

The student will investigate, analyze, and compare square root, cube root, rational, exponential, and logarithmic function families, algebraically and graphically, using transformations.

A2.F.1.aDistinguish between the graphs of parent functions for square root, cube root, rational, exponential, and logarithmic function families.A2.F.1.bWrite the equation of a square root, cube root, rational, exponential, and logarithmic function, given a graph, using transformations of the parent function, including 𝑓(𝑥) + 𝑘; 𝑓(𝑘𝑥); 𝑓(𝑥 + 𝑘); and 𝑘𝑓(𝑥), where 𝑘 is limited to rational values. Transformations of exponential and logarithmic functions, given a graph, should be limited to a single transformation.A2.F.1.cGraph a square root, cube root, rational, exponential, and logarithmic function, given the equation, using transformations of the parent function including 𝑓(𝑥) + 𝑘; 𝑓(𝑘𝑥); 𝑓(𝑥 + 𝑘); and 𝑘𝑓(𝑥), where 𝑘 is limited to rational values. Use technology to verify transformations of the functions.A2.F.1.dDetermine when two variables are directly proportional, inversely proportional, or neither, given a table of values. Write an equation and create a graph to represent a direct or inverse variation, including situations in context.A2.F.1.eCompare and contrast the graphs, tables, and equations of square root, cube root, rational, exponential, and logarithmic functions.
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