1. Section 6.2 – Graphs of Exponential Functions

2. Exponential Functions
𝑓 𝑥 = 𝑎∙𝑏 𝑥 , 𝑎>0
Continuous
One – to – One
Domain: (−∞, ∞)
Range: (0, ∞)
b>1, graph increases
0<𝑏<1, graph decreases
x-axis is a horizontal asymptote
y-intercept: (0, 1)

3. Graphs of Exponential Functions
𝑓 𝑥 = 𝑏 𝑥 ,𝑏>1
𝑓 𝑥 = 𝑒 𝑥
𝑓 𝑥 = 𝑒 𝑥
𝑓 𝑥 = 10 𝑥
𝑓 𝑥 = 10 𝑥
𝑓 𝑥 = 5 𝑥
𝑓 𝑥 = 5 𝑥
𝑓 𝑥 = 2 𝑥
𝑓 𝑥 = 2 𝑥
For the exponential function, 𝑓 𝑥 = 𝑏 𝑥 , where 𝑏>1, the larger the base, the more quickly the graph increases.

4. Graphs of exponential functions
𝑓 𝑥 = 𝑏 𝑥 ,0<𝑏<1
𝑓 𝑥 = 𝑥
𝑓 𝑥 = 𝑥
𝑓 𝑥 = 𝑥
𝑓 𝑥 = 𝑥
𝑓 𝑥 = 𝑥
𝑓 𝑥 = 𝑥
𝑓 𝑥 = 𝑥
𝑓 𝑥 = 𝑥
For the exponential function, 𝑓 𝑥 = 𝑏 𝑥 , where 0<𝑏<1, the larger the base, the flatter the graph.

5. Graphs of Exponential functions
1. 𝑓 𝑥 =− 2 𝑥
Reflect the graph of 𝑓 𝑥 = 2 𝑥 over the 𝑥−axis
Range: (−∞, 0)
Asymptote: 𝑦=0
Range:
Asymptote:

6. Graphs of Exponential functions
2. 𝑓 𝑥 = 𝑥
Range:
Asymptote:
Range: (0, ∞)
Asymptote: 𝑦=0
Stretch the graph of 𝑓 𝑥 = 𝑥 vertically by a factor of 10

7. Graphs of Exponential functions
3. 𝑓 𝑥 = 2 𝑥+1
Shift the graph of 𝑓 𝑥 = 2 𝑥 to the left 1 unit.
Range: (−∞, 0)
Asymptote: 𝑦=0
Range:
Asymptote:

8. Graphs of Exponential functions
4. 𝑓 𝑥 = 2 𝑥 +1
Shift the graph of 𝑓 𝑥 = 2 𝑥 up 1 unit.
Range: (1, ∞)
Asymptote: 𝑦=1
Range:
Asymptote:

9. Graphs of Exponential functions
5. 𝑓 𝑥 = 3 4 −𝑥
Shift the graph of 𝑓 𝑥 = 𝑥 to the right 4 units.
𝑓 𝑥 = 3 −𝑥+4
𝑓 𝑥 = 3 −(𝑥− 4)
𝑓 𝑥 = (𝑥− 4)
Range:
Asymptote:
Range: (0, ∞)
Asymptote: 𝑦=0