M Functions, Lesson 7, Comparing Functions (r. 2018) – FUNCTIONS Comparing Functions CC Standard NG Standard F-IF.C.9 Compare properties of two functions each AI-F.IF.9 Compare properties of two functions each represented in a different way (algebraically, in a different way (algebraically, graphically, numerically in tables, or by verbal in tables, or by verbal descriptions). (Shared standard with Algebra II) For example, given a graph of one quadratic Note: Algebra I tasks are limited to the following function and an algebraic expression for another, linear, quadratic, square root, piecewise defined say which has the larger maximum. (including step and absolute value), and exponential PARCC: Tasks are limited to linear functions, quadratic square root, cube root, piecewise defined (including step functions of the form where > 0 and > 0 (b a b ≠ 1). functions and absolute value functions), and exponential with domains in the integers. LEARNING OBJECTIVES Students will be able to: 1) Compare properties of two functions each represented in a different way. Overview of Lesson Teacher Centered Introduction Student Centered Activities Overview of Lesson guided practice anticipates, monitors, selects, sequences, and Teacher: connects student work - activate students’ prior knowledge - developing essential skills - vocabulary - Regents exam questions - learning objective(s) - formative assessment assignment (exit slip, explain the math, or journal - big ideas: direct instruction entry) - modeling VOCABULARY context graph vertex equation maximum x-intercept four views of a function minimum y-intercept function rule table of values BIG IDEAS Definition of a Function: a function takes the input value of an independent variable and pairs it with one and only one output value of a dependent variable. Function: A function is a relation that assigns exactly one value of the dependent variable to each value of the independent variable. A function is always a relation. Example: y=2x
M – Functions, Lesson 7, Comparing Functions (r. 2018) FUNCTIONS Comparing Functions CC Standard F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, numerically in tables, or by verbal For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. PARCC: Tasks are limited to linear functions, quadratic square root, cube root, piecewise defined (including step functions and absolute value functions), and exponential with domains in the integers. NG Standard AI-F.IF.9 Compare properties of two functions each in a different way (algebraically, graphically, in tables, or by verbal descriptions). (Shared standard with Algebra II) Note: Algebra I tasks are limited to the following linear, quadratic, square root, piecewise defined (including step and absolute value), and exponential functions of the form where a > 0 and b > 0 (b ≠ 1). LEARNING OBJECTIVES Students will be able to: 1) Compare properties of two functions each represented in a different way. Overview of Lesson Teacher Centered Introduction Overview of Lesson - activate students’ prior knowledge - vocabulary - learning objective(s) - big ideas: direct instruction - modeling Student Centered Activities guided practice Teacher: anticipates, monitors, selects, sequences, and connects student work - developing essential skills - Regents exam questions - formative assessment assignment (exit slip, explain the math, or journal entry) VOCABULARY context equation four views of a function function rule graph maximum minimum table of values vertex x-intercept y-intercept BIG IDEAS Definition of a Function: a function takes the input value of an independent variable and pairs it with one and only one output value of a dependent variable. Function: A function is a relation that assigns exactly one value of the dependent variable to each value of the independent variable. A function is always a relation. Example: y=2x
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