Section 6.2 – Graphs of Exponential Functions

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)

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.

Graphs of exponential functions 𝑓 𝑥 = 𝑏 𝑥 ,0<𝑏<1 𝑓 𝑥 = 1 2 𝑥 𝑓 𝑥 = 1 2 𝑥 𝑓 𝑥 = 1 8 𝑥 𝑓 𝑥 = 1 8 𝑥 𝑓 𝑥 = 2 3 𝑥 𝑓 𝑥 = 2 3 𝑥 𝑓 𝑥 = 3 4 𝑥 𝑓 𝑥 = 3 4 𝑥 For the exponential function, 𝑓 𝑥 = 𝑏 𝑥 , where 0<𝑏<1, the larger the base, the flatter the graph.

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:

Graphs of Exponential functions 2. 𝑓 𝑥 =10 1 2 𝑥 Range: Asymptote: Range: (0, ∞) Asymptote: 𝑦=0 Stretch the graph of 𝑓 𝑥 = 1 2 𝑥 vertically by a factor of 10

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:

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:

Graphs of Exponential functions 5. 𝑓 𝑥 = 3 4 −𝑥 Shift the graph of 𝑓 𝑥 = 1 3 𝑥 to the right 4 units. 𝑓 𝑥 = 3 −𝑥+4 𝑓 𝑥 = 3 −(𝑥− 4) 𝑓 𝑥 = 1 3 (𝑥− 4) Range: Asymptote: Range: (0, ∞) Asymptote: 𝑦=0