Let’s solve each problem one by one. We’ll look at the graph, pick points on it, and test which equation fits those points.
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Problem 1:
Graph shows a decreasing curve (going down as x increases). Points marked:
- At x = -2, y = 9 → point (-2, 9)
- At x = -1, y = 3 → point (-1, 3)
- At x = 0, y = 1 → point (0, 1)
Try f(x) = (1/3)^x
→ f(-2) = (1/3)^(-2) = 3^2 = 9
✔
→ f(-1) = (1/3)^(-1) = 3
✔
→ f(0) = (1/3)^0 = 1
✔
Perfect match!
Check others quickly:
f(x) = 3^x → f(-2) = 1/9
✘
f(x) = (1/6)^x → f(-2) = 36
✘
f(x) = 6^x → f(-2) = 1/36
✘
✔ So correct answer is
f(x) = (1/3)^x
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Problem 2:
Graph is increasing. Points:
- (0, 1)
- (1, 2)
- (2, 4)
Try f(x) = 2^x
→ f(0) = 1
✔
→ f(1) = 2
✔
→ f(2) = 4
✔
Others:
f(x) = 1^x → always 1
✘
f(x) = (1/2)^x → decreases
✘
✔ Correct answer:
f(x) = (2)^x
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Problem 3:
Graph increasing. Points:
- (0, 1)
- (1, 2)
- (2, 4)
Same as Problem 2! Try f(x) = 2^x
→ f(0)=1, f(1)=2, f(2)=4
✔
Options include f(x)=(2)^x — that’s there.
Wait — options also have f(x)=(1)^x twice? Probably typo, but we ignore wrong ones.
✔ Correct answer:
f(x) = (2)^x
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Problem 4:
Graph decreasing sharply. Points:
- (-2, 25)
- (-1, 5)
- (0, 1)
Try f(x) = (1/5)^x
→ f(-2) = (1/5)^(-2) = 5^2 = 25
✔
→ f(-1) = (1/5)^(-1) = 5
✔
→ f(0) = 1
✔
Try f(x) = (1/10)^x → f(-2)=100
✘ too big
f(x)=5^x → f(-2)=1/25
✘
f(x)=10^x → f(-2)=1/100
✘
✔ Correct answer:
f(x) = (1/5)^x
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Final Answer:
1. f(x) = (1/3)^x
2. f(x) = (2)^x
3. f(x) = (2)^x
4. f(x) = (1/5)^x
Parent Tip: Review the logic above to help your child master the concept of graph exponential function worksheet.
