Lesson 3 Absolutely Valuable Solidify Understanding
Relate piecewise functions to absolute value.
Identify features of an absolute value function.
What is the effect of taking the absolute value of a linear function?
How can we think of absolute value as a function?
Open Up the Math: Launch, Explore, Discuss
Michelle likes riding her bike to and from her favorite lake on Wednesdays. She created the following graph to represent the distance she is away from the lake while biking.
Interpret the graph by writing three observations about Michelle’s bike ride.
Write a piecewise function for this situation, with each linear function being in point-slope form using the point
This particular piecewise function is called a linear absolute value function. What are some of the characteristics of linear absolute value functions that you see in this graph?
In this part of the task, you will solidify your understanding of piecewise functions and reason about absolute value functions.
Complete the table of values from
On the same set of axes, using a different-colored pencil, graph
Explain the difference in the graphs of
Use the graph to write the piecewise function for
What similarities and differences do you observe in the piecewise form of
The function is sometimes written in piecewise form and often written as
Answer each question below and explain your answer.
What is the domain of
What is the range of
What is the minimum of
Based on your analysis, how would you write the piecewise function that modeled Michelle’s bike ride in absolute value form?
Ready for More?
Besides Michelle’s bike ride, what is another context that could be modeled by an absolute value function?
Graph:The absolute value function:
In this lesson, we learned about the linear absolute value function. We learned that absolute value functions can be written as piecewise functions or using the operation because they have two distinct parts. We identified the domain and range and graphed the function.
Explain how the given function compares to the parent function,
Evaluate the given expression using the variable provided.