Unit 2: Linear &
Exponential Functions
Lesson Video
Focus Standards
Learning Focus
Additional Resources
A Develop Understanding Task
Introduces linear and exponential functions as broad classes of functions that may be continuous or discrete. Develops the concept of domain.
Represent situations with different types of growth.
Compare models for situations that occur over time.
What type of situation can be modeled by a continuous graph? When is a graph of only separate points appropriate?
What are the similarities and differences between an arithmetic sequence and a linear function?
Can a geometric sequence be continuous?
A Solidify Understanding Task
Solidifies understanding of the differences in discrete and continuous models for linear and exponential functions. Introduces how to write domains using set builder notation.
Use representations to model situations with linear and exponential functions.
Determine when a discrete model or continuous model is most appropriate.
What is the difference between discrete and continuous functions?
How can I tell if a discrete or continuous model is best for a given situation?
Are all linear functions continuous? Are all arithmetic sequences discrete?
Are all exponential functions continuous? Are all geometric sequences discrete?
How is the domain related to whether the function is continuous or discrete?
Lesson 3: The Name Game
A Solidify Understanding Task
Combines identifying linear and exponential functions with distinguishing between discrete and continuous representations.
Use representations to determine if a function is discrete or continuous.
Determine the domain of a function.
How can I tell if a function is linear or exponential, given any representation?
How can I think about a constant rate of change or a constant ratio if a function is continuous?
Why are arithmetic sequences linear functions?
Why are geometric sequences exponential functions?
Lesson 4: Twin Powers
A Solidify Understanding Task
Reinforces reasoning with positive and negative rational exponents.
NC.M1.N-RN.2
Relate the key features of exponential functions to properties of negative exponents.
Rewrite exponential expressions that involve negative exponents.
How does my understanding of the properties of exponents help me explain the key features of exponential functions?
How does my understanding of the properties of exponents help me rewrite exponential expressions that contain negative exponents?
Lesson 5: The Power of Negative Thinking
A Practice Understanding Task
Uses rules of exponents to simplify algebraic expressions with integer exponents.
NC.M1.N-RN.2
Change the form of algebraic expressions using properties of exponents.
How do the properties of exponents help explain methods for changing the form of algebraic expressions, including fractions?
A Solidify Understanding Task
Compares the growth of linear and exponential functions and uses mathematical models to make decisions and predictions.
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Make modeling decisions about business plans.
Interpret mathematical models to make business decisions.
Determine which type of function grows faster and make arguments about why.
Which type of function increases faster—linear or exponential?
Which model is best for a given situation, discrete or continuous?
How can mathematical models help to make business decisions?
A Practice Understanding Task
Uses average rate of change to find growth in a given interval of a non-linear function.
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Understand and find the average rate of change of a function in an interval.
Develop a formula for the average rate of change for any function.
How can I find the average rate of change of a function that is not linear?
What does the average rate of change mean?
Lesson 8: Point the Way
A Solidify Understanding Task
Introduces point-slope form of the equation of a line to write equations.
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Find patterns that are useful in writing equations for linear functions.
Are there different ways to write the equation of a line?
What does each part of an equation tell us?
Lesson 9: Form Follows Function
A Practice Understanding Task
Builds fluency and flexibility in working with linear and exponential functions and their forms.
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Use different forms of linear and exponential functions to efficiently write equations.
Use the information given in different forms of equations to graph functions.
How do I use forms of equations for graphing linear and exponential functions?
What is the purpose of having different forms of equations?
How do I choose which form is most efficient?