Lesson 1 Winner, Winner Develop Understanding
Learning Focus
Understand the behavior of
Graph and describe the features of
How can winning the lottery help us to think about
What features make
Open Up the Math: Launch, Explore, Discuss
One of the most interesting functions in mathematics is
Let’s begin by thinking about the interval
1.
Imagine that you won the lottery and were given one big pot of money. Of course, you would want to share the money with friends and family. If you split the money evenly between yourself and one friend, what would be each person’s share of the prize money?
2.
If three people shared the prize money, what would be each person’s share?
3.
Model the situation with a table, equation, and graph.
4.
Just in case you didn’t think about the really big numbers in your model, how much of the prize would each person get if
5.
Use mathematical notation to describe the behavior of this function as
Next, let’s look at the interval
6.
Imagine that you want each person’s share to be
7.
If you want each person’s share to be
8.
Model this situation with a table, equation, and graph.
9.
What do you notice when you compare the two models that you have written?
Now, let’s put it all together to graph the entire function,
10.
Create a table for
11.
How do the values of
12.
Graph
13.
Describe the features of
Ready for More?
How would you explain to a friend why
Takeaways
Features of
Interval | |
Interval | |
Characteristics | |
Symmetry | |
End behavior | |
Asymptotes | |
Domain | |
Range | |
Intervals of decrease | |
Intercepts, maximum, minimum |
Vocabulary
- asymptote
- horizontal asymptote
- vertical asymptote
- Bold terms are new in this lesson.
Lesson Summary
In this lesson, we learned about the function
1.
Describe the transformation of this function from
2.
Write the equation of this exponential function. Then write the equation of the horizontal asymptote.