Exploring Exponential Functions

In class on Friday we did a graphing activity called exploring exponential functions. In the activity we graphed different sets of equations that all were the same except 1 or 2 factors were changed to figure out what the different elements did to the graph.

In set 1, a and b were the same but c varied. From this we figured out that c moves the graph up and down. To figure out the y-intercept you can use the equation (when y is the intercept) c+a=y.

In set 2, b and c stayed the same but b varied. The higher b was, the higher the y-intercept was. The graphs look similar except that the graph accelerates faster to start out when the a is higher.

In set 3, the only thing that changed was the growth factor which effected how fast the slope grew and moreover the steepness of the graph. The higher the growth factor the steeper the graph.

Finally, in set four we explored a fraction as a growth factor and a negative. When the growth factor is a fraction the slope starts out large and gets smaller and smaller as the x continues. When the growth factor is negative the graph goes down instead of up and mirrors whatever the graph would be if the growth factor were not a negative.