8.3.7: 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.

8.3.7.01Compare graphical properties of proportional and non-proportional linear relationships, including slope.8.3.7.02Analyze visual patterns to distinguish between linear and non-linear patterns. For linear patterns, describe how a pattern is changing, name the nth term and write an equation to generalize the nth term.8.3.7.03Recognize that a function is a rule that assigns each input to exactly one output. Use the function to represent the relationship in which changing the input (independent) variable, by an amount, leads to a change in the output (dependent) variable, a constant multiplied by that amount. Recognize that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Use functional notation, such as f(x), to represent such relationships.8.3.7.04Represent linear functions with tables, verbal descriptions, symbols, equations and graphs. Translate from one representation to another.8.3.7.05Explain how changes to the values m or b in the linear function f(x) = mx + b affect the graph of the function. Use graphing technology to examine these effects. Recognize that the graph of the linear equation y = mx + b comes from b units translation of y = mx graph.8.3.7.06Identify graphical properties of linear functions in the form f(x) = mx + b, including slope, y-intercept and x-intercept. Know that the graph is a straight line, the slope (m) equals the rate of change, the y-intercept (b) is the value of the function at x = 0 and the x-intercept is the value of the function at f(x) = 0.8.3.7.07Recognize that an arithmetic sequence is a linear function that can be expressed in the form f(x) = mx + b, where x = 0, 1, 2, 3,....8.3.7.08Recognize that a geometric sequence is a non-linear function that can be expressed in the form f(x) = a(b)^x, where x = 0, 1, 2, 3,....8.3.7.09Represent arithmetic and geometric sequences using equations, tables, graphs and verbal descriptions and use them to solve situations.

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