9.3.7: Patterns and Relationships: Represent and connect mathematical patterns and relationships using verbal descriptions, generalizations, tables and graphs. Use representations to generate questions, make predictions and solve mathematical problems.

Patterns and Relationships: Represent and connect mathematical patterns and relationships using verbal descriptions, generalizations, tables and graphs. Use representations to generate questions, make predictions and solve mathematical problems.

9.3.7.01Represent and solve situations in various contexts, including financial literacy, using systems of linear equations, systems of linear inequalities and exponential and quadratic functions. (MP4)9.3.7.02Translate between graphs of quadratic, exponential and other functions (including absolute value, rational and polynomial), tables and symbolic representations. Sketch graphs and use graphing technology to graph functions. (MP5)9.3.7.03Determine how vertical/horizontal reflecting, translating and scaling affect the symbolic and graphical forms of a function. Use graphing technology to examine transformations. (MP3)9.3.7.04Express the terms in an arithmetic or geometric sequence recursively and by giving an explicit formula. (MP8)9.3.7.05Express recursive patterns using recursive formulas. Calculate sequences defined by recursive formulas. (MP8)9.3.7.06Find the domain and range of functions defined symbolically, graphically or in a context, including piecewise and step functions. Express solutions and recognize that some answers obtained may not be valid, including cases where the function inputs are discrete instead of continuous. (MP4)9.3.7.07Describe the graph of a function using key features such as intercepts, maxima/minima, intervals of increase and decrease and end behavior. Draw conclusions from graphs of functions and other relations. (MP3)9.3.7.08Define the compounding of interest n times per year according to a recursive formula. Compare the recursive definition of interest to the recursive definition of a geometric sequence t(n) = r(t(n - 1)). Compare the interest formula A = P(1 + r/n)^nt to the general form of an exponential function y = a(b)^x. Explain the purpose of each part of the interest formula. (MP4, MP5)9.3.7.09Find the inverse of a given function and justify the results using tables, graphs or algebra. (MP4, MP6)9.3.7.10Use the concept of a function as a connection between inputs and outputs to find function values and use function notation. (MP2)

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