Exploring Exponential Functions
For this activity, you are going to see what happens when we manipulate the parent function . There are three parameters, or values that you can change that affect the shape and location of the graph of our function. Follow the instructions for each section and answer the questions that follow.
Part 1
For this first part, set the following values:
a = 1
h = 0
k = 0
Our simplified function is now . Play with the b slider and answer the questions below.
What do you notice changes when you change the b slider? Are there any values where you notice specific things happening?
What do you notice stays the same when you change the b-value?
Part 2
Now set these values:
a = 1
b = 2
h = 0
Our function is now . Slide the k slider and answer the following question.
What do you see happening when you move the k slider? Can you use mathematical vocabulary to say what the k-value tells us about ?
Part 3
Now set these values:
a = 1
b = 2
k = 0
Our function is now . Slide the h slider and answer the question below.
What happens when you move the h slider?
Part 4
Set these values:
b = 2
h = 0
k = 0
Our function is now . Play with the a slider and answer the questions below.
What do you notice changing as you slide the a slider?
Look at the graphs of and . How do these compare?
Part 5
In the final part, you can adjust more than one slider at a time and see how they interact with one another. Once you have a graph you like (please make sure that you do not set a to 0, or b to 0 or 1), answer the questions below.
Write out your function algebraically.
Why did I not want you to set a = 0, b = 0, or b = 1?
Is your function an example of exponential growth or decay? Explain your answer.