COMPARING LINEAR AND NONLINEAR FUNCTIONS

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1 1 COMPARING LINEAR AND NONLINEAR FUNCTIONS LEARNING MAP INFORMATION STANDARDS 8.F.2 Compare two s, each in a way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a by a table of values a by an algebraic expression, determine which has the greater change. 8.F.3 Interpret the equation y = mx + b as defining a, whose graph is a straight line; give examples of s that are not. For example, the A = s 2 giving the area of a square as a of its side length is not because its graph contains the points (1,1), (2,4) (3,9), which are not on a straight line. s change in an algebraic y-intercept slope a constant s slope-intercept the same the s s compare 2 s with rates of change 2 s in the same 2 s in

2 2 8.F.2 Compare two s each in a way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a by a table of values a by an algebraic expression, determine which has the greater change. determine a unit rate given an equation change in a table change in a graph change in an algebraic s slope constant a y-intercept s the same s compare 2 s with rates of change 2 s in the same 2 s in

3 3 8.F.3 Interpret the equation y = mx + b as defining a, whose graph is a straight line; give examples of s that are not. For example, the A = s 2 giving the area of a square as a of its side length is not because its graph contains the points (1,1), (2,4) (3,9), which are not on a straight line. slope-intercept the s s

4 4 Node Name ANALYZE LINEAR FUNCTIONS ANALYZE THE SAME FUNCTION IN 2 OR MORE DIFFERENT FORMS COMPARE THE PROPERTIES OF 2 FUNCTIONS REPRESENTED IN DIFFERENT FORMS COMPARE THE PROPERTIES OF 2 FUNCTIONS REPRESENTED IN THE SAME FORM COMPARE 2 FUNCTIONS WITH DIFFERENT RATES OF CHANGE DESCRIBE THE RATE OF CHANGE IN A GRAPH DESCRIBE THE RATE OF CHANGE IN A TABLE DESCRIBE THE RATE OF CHANGE IN AN ALGEBRAIC FUNCTION DETERMINE A UNIT RATE GIVEN AN EQUATION EXPLAIN CONSTANT FUNCTION EXPLAIN INCREASING AND DECREASING LINEAR FUNCTIONS Node Description Analyze a in any representation (e.g., a graph, a table, an algebraic equation, or a description) by identifying ing local properties (e.g., intercepts values at given points) global properties (e.g., the slope/ change the direction of covariation). Analyze the one in (e.g., a graph, a table, an algebraic equation, or a description). Compare the properties (e.g., domain, range, change, overall shape) of two s in ways (e.g., algebraically, graphically, numerically in tables, or verbally in descriptions). Compare the properties (e.g., change, intercepts, direction of a covariation, or overall shape) of two s in the same way (e.g., algebraically, numerically in tables, graphically, or verbally in descriptions). Compare two s with rates of change to communicate which is faster or slower or is higher or lower. Describe the change in a graph by quantifying the Describe the change in a table by quantifying the Describe the change in an algebraic by quantifying the Trans a given equation to determine the rate at which one variable changes in terms of one unit of another variable. etc., that a constant has a zero slope its graph is a straight, horizontal line. etc., that an has a positive slope a has a negative slope. EXPLAIN LINEAR FUNCTION etc., that a changes at a constant rate its graph is a straight line. EXPLAIN SLOPE EXPLAIN SLOPE-INTERCEPT FORM EXPLAIN Y-INTERCEPT RECOGNIZE A FUNCTION REPRESENTED IN 2 OR MORE DIFFERENT FORMS RECOGNIZE FUNCTION etc., that the slope of a line is the steepness of the line as a ratio. Describe slope as rise over run or the change in y divided by the change in x. etc., that a can be described by its slope-intercept (y = mx + b), which consists of the slope, m, the y-intercept, b. etc., that the y-intercept is a coordinate pair where the graph of a intersects the y-axis. etc., that a can be modeled in two or more. Recognize a as a set of ordered pairs where there exists a relationship between x- y-coordinates there are no two ordered pairs with the same input outputs.

5 5 Node Name RECOGNIZE INCREASING AND DECREASING FUNCTIONS RECOGNIZE LINEAR FUNCTION RECOGNIZE THE PROPERTIES OF FUNCTIONS Node Description Identify or name an as a with a graph that rises from left to right over the entire domain. Identify or name a as a with a graph that falls from left to right over the entire domain. Identify or name a, when a is non. Determine underst the local properties (e.g., intercepts max/min) global properties (e.g., domain, direction of covariance, end behavior) of a in any. ADDITIONAL NODES RELATED TO THIS UNIT OF INSTRUCTION Node Name Node Description Related Node RECOGNIZE COVARIATION Recognize the change that occurs in the dependent variable when the independent variable is changed. Prerequisite of EXPLAIN SLOPE (through RECOGNIZE THE DIRECTION OF A COVARIATION) RECOGNIZE Y-INTERCEPT Identify or name the y-intercept as a point on the y-axis. Prerequisite of EXPLAIN Y-INTERCEPT

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