Unit 5
COMPARING & CONTRASTING FUNCTIONS
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Unit 5 Study Guide  
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I Can Statements  Unit 5  
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IN THIS UNIT STUDENTS WILL BE EXPECTED TO:
 Construct and compare linear and exponential models and solve problems.
 Recognize situations with constant rates of change as well as those in which a quantity either grows or decays by a constant
percent rate.
 Given a contextual situation, describe whether the situation in question has a linear pattern of change or an exponential pattern of
change.
 Write a recursive and an explicit formula for arithmetic and geometric sequences.
 Understand that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more
generally) any polynomial function.
 Interpret and understand the quantities (m and b), rates of change, and other values of a linear function f(x) = mx + b in the
context of a realworld scenario.
 Interpret and understand the quantities (a, b, and c), rates of change, and other values of an exponential function f(x) = a * bx + c
in the context of a realworld scenario.
 Describe the effect of transformations on functions and their graph.
 Understand and utilize function notation to describe data in a table or graph.
 Understand how function notation can be applied to real world problems.
 Graph a function that algebraically models a relationship between two quantities and interpret the graphs’ key characteristics:
 x and y intercepts  ordered pairs  increasing intervals  decreasing intervals
 positive intervals  negative intervals  relative maximums  relative minimums
 symmetries  positive end behavior  negative end behavior  periodicity
 Explain the difference and relationship between domain and range and find the domain and range of a function from a function
equation, table or graph.
 Calculate and interpret the average rate of change of a function presented in symbolically and a table over a specified interval.
 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by
verbal descriptions).
 Construct and compare linear and exponential models and solve problems.
 Recognize situations with constant rates of change as well as those in which a quantity either grows or decays by a constant
percent rate.
 Given a contextual situation, describe whether the situation in question has a linear pattern of change or an exponential pattern of
change.
 Write a recursive and an explicit formula for arithmetic and geometric sequences.
 Understand that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more
generally) any polynomial function.
 Interpret and understand the quantities (m and b), rates of change, and other values of a linear function f(x) = mx + b in the
context of a realworld scenario.
 Interpret and understand the quantities (a, b, and c), rates of change, and other values of an exponential function f(x) = a * bx + c
in the context of a realworld scenario.
 Describe the effect of transformations on functions and their graph.
 Understand and utilize function notation to describe data in a table or graph.
 Understand how function notation can be applied to real world problems.
 Graph a function that algebraically models a relationship between two quantities and interpret the graphs’ key characteristics:
 x and y intercepts  ordered pairs  increasing intervals  decreasing intervals
 positive intervals  negative intervals  relative maximums  relative minimums
 symmetries  positive end behavior  negative end behavior  periodicity
 Explain the difference and relationship between domain and range and find the domain and range of a function from a function
equation, table or graph.
 Calculate and interpret the average rate of change of a function presented in symbolically and a table over a specified interval.
 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by
verbal descriptions).