Graph Options

8
advanced-math

Which graph represents the function y=3(0.8)xy = 3(0.8)^x?

A

Graph with y-intercept 3, decreasing

B

Graph with y-intercept 3, increasing

C

Graph with y-intercept 0.8, decreasing

D

Graph with y-intercept 0.8, increasing

Correct Answer: A

Choice A is the correct answer. Analyze the initial value and direction.

  1. Initial Value: When x=0x=0, y=3(0.8)0=3y = 3(0.8)^0 = 3, so y-intercept is 3.
  2. Base: 0.8<10.8 < 1 means the function is decaying (decreasing).
  3. Match: Graph with y-intercept 3 and decreasing curve.

💡 Strategic Tip: If b<1b < 1, the graph decreases (decay). If b>1b > 1, it increases (growth).

Choice B is incorrect because the base 0.8 < 1 means decay, not growth. Choice C is incorrect because the y-intercept is 3, not 0.8. Choice D is incorrect because both the y-intercept and direction are wrong.