10
advanced-math

The table shows data from two functions:

xxf(x)f(x)g(x)g(x)
01010
12015
24020

Which statement is true?

A

f(x)f(x) is exponential, g(x)g(x) is linear

B

f(x)f(x) is linear, g(x)g(x) is exponential

C

Both are exponential

D

Both are linear

Correct Answer: A

Choice A is the correct answer. Check ratios and differences.

  1. f(x)f(x): Ratios 2010=2\frac{20}{10}=2, 4020=2\frac{40}{20}=2 → Exponential (base 2).
  2. g(x)g(x): Differences 1510=515-10=5, 2015=520-15=5 → Linear (slope 5).
  3. Conclusion: f(x)f(x) is exponential, g(x)g(x) is linear.

💡 Strategic Tip: Constant ratios = exponential. Constant differences = linear.

Choice B is incorrect because it reverses the classifications. Choice C is incorrect becauseg(x)g(x) has constant differences. Choice D is incorrect becausef(x)f(x) has constant ratios.