Lesson 1E Winner, Winner Develop Understanding
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
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?
If three people shared the prize money, what would be each person’s share?
Model the situation with a table, equation, and graph.
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
Use mathematical notation to describe the behavior of this function as
Next, let’s look at the interval
Imagine that you want each person’s share to be
If you want each person’s share to be
Model this situation with a table, equation, and graph.
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,
Create a table for
How do the values of
Describe the features of
Ready for More?
How would you explain to a friend why
Intervals of decrease
Intercepts, maximum, minimum
In this lesson, we learned about the function
Describe the transformation of this function from
Write the equation of this exponential function. Then write the equation of the horizontal asymptote.