ESSENTIAL QUESTION
Common Core Standards
2017-2018
Print Unit 2

What are the basic common parent functions?

High School - Math - Algebra I - Unit 2

Parent Functions

Linear, constant, quadratic, cubic, square root, cube root, rational, logarithmic and exponential partent fucntions and the characterstics of their equations and graphs are investigated. Transformations of those graphs and the resulting modifications to the parent equation are studied. The focus of the unit is a holtistic approach to the examination of fucntion features.

OVERVIEW
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The introductory unit on Parent Functions will focus on the analysis of key features of graphs and equations and enable the students to examine functions throughout the course in a holistic fashion.

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COMMON CORE STANDARDS
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**F-IF 4.**For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

*Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; & periodicity.*

**F-IF 5.**Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

**F-IF 7.**Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

**F-IF 8**. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

b. Use the properties of exponents to interpret expressions for exponential functions.

**F-IF 9.**Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

**F-BF 3.**Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x+k) for specific values of

*k*(both positive and negative); find the value of

*k*given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

STUDENT LEARNING TARGETS
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I can define a function that relates two quantities.

I can define the key features of a function:

*intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*I can sketch/interpret the graph of a relationship between two quantities.

I can use a verbal representation of a function to create its graph.

I can determine the domain of a function.

I can connect the domain of a function to its graph.

I can use the domain to determine appropriate scale and units for the graph of a function.

I can define x- intercepts, y-intercepts, minima and maximum.

I can graph linear, absolute value, quadratic and exponential function and identify their key characteristics.

I can relate coefficients of a linear equation and the slope and x- and y-intercepts of its graph.

I can graph a quadratic function and understand the relationship between its real zeros and the x-intercepts of the graph.

I can define square root, cube root, piecewise, step, and absolute value functions.

I can identify parent functions.

I can graph by hand or with technology square root, cube root, piecewise, step, and absolute value functions.

I can compare the properties of classes of functions.

I can define a polynomial function.

I can describe the zeros of a polynomial function.

I can define the end behavior.

I can recognize the connection among zeros of a polynomial function,

*x*-intercepts, factors of polynomials, and solutions of polynomial equations.I can use technology to graph a polynomial function and approximate the zeros, minimum, and maximum; determine domain and range of the polynomial function.

I can determine the end behavior for a polynomial function.

I can graph exponential functions.

I can graph logarithmic functions.

I can describe different representations of a function.

I can define zero, extreme values, and symmetry of a graph for a quadratic function.

I can classify a function as representing exponential growth and decay.

I can describe the graph of a quadratic function and understand the relationship between its real zeros and the x-intercepts of the graph.

I can understand and compare the properties of classes of functions (e.g. absolute value, step, exponential, polynomial, rational, logarithmic, and periodic).

I can identify the properties of function (algebraically, graphically, numerically in tables, or by verbal description).

I can compare two functions, each represented in different ways.

I can identify effects of single transformations on graphs of functions, with or without technology.

I can graph a given function by replacing f(x) by f(x) + k, kf(x), f(kx), and f(x+k) for specific values of

*k*(both positive and negative).I can describe the differences and similarities between a parent function and the transformed function.

I can find the value of k, given the graphs a parent function and a transformed function).

I can experiment with cases and illustrate an explanation of the effects on the graph using technology.

CRITICAL VOCABULARY
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Function, Domain, Range, Graph, Equation, Increasing, Decreasing, Interval, Right-End Behavior, Left-End Behavior, Continuity, Discontinuity, Horizontal Asymptote, Vertical Asymptote, Extremes, Minimum, Maximum, Transformation, X-Intercept, Y-Intercept, Axis, Symmetry, Linear, Constant, Quadratic, Cubic, Square Root, Cube Root, Rational, Logarithmic, Exponential, Growth Function, Decay Function

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LEARNING EXPERIENCES
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Educator Uploaded Plans
(These are educators specific templates with included information and specifics)

E-TOOLS
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RESOURCES
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parent fucntion class visuals, textbook, TI-84 graphing calculator, zoom math, geometry sketchpad

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LITERACY STRATEGIES
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THOUGHTFUL EDUCATION TOOLS
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