Powerpoint with activating lesson, lesson, and references to assessments (GPS Georgia Mathematics I: Test Prep and Practice) for Unit 1, Lesson 1 for Math I. Concepts: Family of Functions: Linear, Absolute Value, Quadratic, Cubic, Radical, and Rational Skills: MM1A1.a How do we represent functions using function notation? MM1A1.b How do we graph and write equation for each of the Family of Functions? MM1A1.c How do we graph transformations of functions? MM1A1.d What are the characteristics of a function and how do you use them? MM1A1.e How do we use graphs and tables to investigate behavior of functions? MM1A1.f How do we recognize sequences as functions with domains that are whole numbers? MM1A1.g How do constant rates of change compare to variable rates of change within the Family of Functions? MM1A1.h How do we determine graphically and algebraically whether a function has symmetry and whether it is odd, even, or neither? MM1A1.i How do we interpret an equation in x, and its solutions as f(x) = g(x) and show where they intersect? Identify functions by graph and equation B. Identify critical points and slope C. Identify characteristics: Domain and range, zeros and intercepts, max and min, end behavior, and increase and decrease C. Graph equation D. Write equations from graph E. Identify parent graphs. Learning Activities: Methods: Procedures:

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- Mathematics > Algebra

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Represent functions using function notation.

Graph the basic functions f(x) = x to the n power, where n = 1 to 3, f(x) = the square root of x, f(x) = |x|, and f(x) = 1/x.

Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

Recognize sequences as functions with domains that are whole numbers.

Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).