Section 6.4: Graphing Exponentials
Exponential functions can be graphed by identifying the base \( b \), the initial value \( a \), and plotting points for several x-values.
Example 1
Graph \( f(x) = 2^x \) for \( x = -2, -1, 0, 1, 2 \)
Compute points: \( f(-2)=1/4, f(-1)=1/2, f(0)=1, f(1)=2, f(2)=4 \)
Plot points and draw a smooth curve through them showing exponential growth.
Example 2
Graph \( g(x) = (1/3)^x \) for \( x = -2, -1, 0, 1, 2 \)
Compute points: \( g(-2)=9, g(-1)=3, g(0)=1, g(1)=1/3, g(2)=1/9 \)
Plot points and draw a smooth curve through them showing exponential decay.
Practice Problems
- Graph \( f(x) = 3^x \) for \( x = -2, -1, 0, 1, 2 \)
- Graph \( g(x) = (1/2)^x \) for \( x = -2, -1, 0, 1, 2 \)
- Graph \( h(x) = 5 \cdot 2^x \) for \( x = 0, 1, 2, 3 \)
- Graph \( k(x) = 1/4 \cdot (3)^x \) for \( x = -1, 0, 1, 2 \)
- Identify whether \( m(x) = 2 \cdot (1/5)^x \) is growth or decay and graph it