I'll help you solve this exponential functions graphing worksheet. Let me work through each function step by step, creating tables of values and understanding how to graph them.
Let me start by working through each of the 6 exponential functions:
1. y = 4^x
- When x = -2: y = 4^(-2) = 1/16 = 0.0625
- When x = -1: y = 4^(-1) = 1/4 = 0.25
- When x = 0: y = 4^0 = 1
- When x = 1: y = 4^1 = 4
- When x = 2: y = 4^2 = 16
2. y = (1/3)^x
- When x = -2: y = (1/3)^(-2) = 3^2 = 9
- When x = -1: y = (1/3)^(-1) = 3^1 = 3
- When x = 0: y = (1/3)^0 = 1
- When x = 1: y = (1/3)^1 = 1/3 ≈ 0.33
- When x = 2: y = (1/3)^2 = 1/9 ≈ 0.11
3. y = 0.75^x
- When x = -2: y = 0.75^(-2) = (1/0.75)^2 = (4/3)^2 = 16/9 ≈ 1.78
- When x = -1: y = 0.75^(-1) = 1/0.75 = 4/3 ≈ 1.33
- When x = 0: y = 0.75^0 = 1
- When x = 1: y = 0.75^1 = 0.75
- When x = 2: y = 0.75^2 = 0.5625
4. y = 2·3^x
- When x = -2: y = 2·3^(-2) = 2·(1/9) = 2/9 ≈ 0.22
- When x = -1: y = 2·3^(-1) = 2·(1/3) = 2/3 ≈ 0.67
- When x = 0: y = 2·3^0 = 2·1 = 2
- When x = 1: y = 2·3^1 = 2·3 = 6
- When x = 2: y = 2·3^2 = 2·9 = 18
5. y = (1/2)·2^x
- When x = -2: y = (1/2)·2^(-2) = (1/2)·(1/4) = 1/8 = 0.125
- When x = -1: y = (1/2)·2^(-1) = (1/2)·(1/2) = 1/4 = 0.25
- When x = 0: y = (1/2)·2^0 = (1/2)·1 = 0.5
- When x = 1: y = (1/2)·2^1 = (1/2)·2 = 1
- When x = 2: y = (1/2)·2^2 = (1/2)·4 = 2
6. y = 6·(1/2)^x
- When x = -2: y = 6·(1/2)^(-2) = 6·2^2 = 6·4 = 24
- When x = -1: y = 6·(1/2)^(-1) = 6·2^1 = 6·2 = 12
- When x = 0: y = 6·(1/2)^0 = 6·1 = 6
- When x = 1: y = 6·(1/2)^1 = 6·(1/2) = 3
- When x = 2: y = 6·(1/2)^2 = 6·(1/4) = 1.5
Now let me verify my calculations more carefully:
Parent Tip: Review the logic above to help your child master the concept of exponential functions and their graphs worksheet.
