standard_description: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
problem_activity: Warm-up
The purpose of this warm-up is to encourage students to connect the ideas they learned earlier about statistical questions and types of data (categorical and numerical) to the work on describing distributions (center and spread).
There are many ways to interpret the questions and identify how each one is unique. For example, they could say that Question A is about retirement, Question B about jobs, etc. If students begin to depart from thinking in statistical terms, remind them to think about how we might go about answering the questions and what the answers might involve.
Launch
Arrange students in groups of 2–4. Display the questions for all to see. Give students 1 minute of quiet think time and ask students to indicate when they have noticed one question that does not belong and can explain why. When the minute is up, give students 2 minutes to share with their group their reasoning on why a question doesn't belong, and then, together, find at least one reason each question doesn't belong.
Student Facing
Here are four questions about the population of Alaska. Which question does not belong? Be prepared to explain your reasoning.
In general, at what age do Alaska residents retire?
At what age can Alaskans vote?
What is the age difference between the youngest and oldest Alaska residents with a full-time job?
Which age group is the largest part of the population: 18 years or younger, 19–25 years, 25–34 years, 35–44 years, 45–54 years, 55–64 years, or 65 years or older?
Student Response
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Activity Synthesis
Ask each group to share one reason why a particular question does not belong. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer for why a question does not belong, attend to students’ explanations and ensure the reasons given are correct.
If students use terms that are essential in this unit (such as center, spread, statistical, non-statistical, numerical data, categorical data, etc.), ask them to explain their meanings in their own words; these are opportunities to reinforce their understanding of the terms and to note any misconceptions. If students give unsubstantiated claims, ask them to substantiate them.


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