1. Graph Exponential Functions

2. exponential functions
Remember that Exponential Functions:
Take the form y = abx (or y = ax m)
Graph as a smooth curve
‘growth’ = increasing
‘decay’ = decreasing
they will get big fast!
like geometric sequences

3. Exponential Functions

4. Graph Exponential Functions-3 -2 -1 1 2 3
2-3 = = 1 8
1 8
Sketch the graph of y = 2x
2-2 = = 1 4
1 4
Make a table of values
(be careful with your exponent rules)
Plot them on a graph
Connect with a smooth curve
(Remember the asymptote! Don’t let your curve go totally straight, but also don’t let it keep going down forever)
2-1 = = 1 2
1 2
20=1 1
21=2 2
22=4 4
23=8 8
Since y=abx then here it is y=(1)(2)x so the y-int is 1 and the constant ratio is 2 (notice the y values in table are doubling)
Will it ever touch the x-axis?

5. Graph Exponential Functions-3 -2 -1 1 2 3
2-3 =
4 1 8
Sketch the graph of y = 2x + 4
2-2 =
4 1 4
Make a table of values
(be careful with your exponent rules)
Plot them on a graph
Connect with a smooth curve
(Remember the asymptote! Here it will be the line y=4. Why?)
2-1 =
4 1 2
20=1+4 5
21=2+4 6
22=4+4 8
23=8+4 12

6. sketching an accurate curve
Remember the asymptote!
Don’t let your curve go totally straight, but also don’t let it keep going down forever

7. Graph Exponential Functions-3 -2 -1 1 2 3
3-3 = = 1 27
1 27
Sketch the graph of y = 3x
3-2 = = 1 9
1 9
Make a table of values
(be careful with your exponent rules)
Plot them on a graph
Connect with a smooth curve
(Remember the asymptote! Don’t let your curve go totally straight, but also don’t let it keep going down forever)
3-1 = = 1 3
1 3
30=1 1 3 9 27
Will it ever touch the x-axis?

8. Graph Exponential Functions-3 -2 -1 1 2 3
( 𝟏 𝟐 )-3 = 1−3 2−3 = =8 8
Sketch the graph of y = ( 1 2 )x 4
( 𝟏 𝟐 )-2 = 1−2 2−2 = =4 2
Make a table of values
(be careful with your exponent rules)
Plot them on a graph
Connect with a smooth curve 1
( 𝟏 𝟐 )-1 = 1−1 2−1 = =2
1 2
1 4
1 8
How can you predict from the function that this is a decreasing graph?