Question

The functions f(x) and g(x) are shown below:

f(x) = (0.001)^x
g(x) = 0.001x

Which statement best describes the graph of f(x) and g(x)?

Answer 1

(A) The graph of g(x) will eventually exceed the graph of f(x).
(B) The graph of f(x) will eventually exceed the graph of g(x).
(C) The graphs will both have their y-intercept equal to 1.
(D) The graphs will both have their y-intercept equal to 0.001.

Answer 2

@dan815 @TheSmartOne Can you guys help me out?

Answer 3

plug in x = 0 into each function. What do you get?

Answer 4

f(x) is an exponential decay function, right?

Answer 5

yes because the base is less than 1 (and still positive)

Answer 6

f(x) = 1 when x = 0. g(x) = 0 when x = 0

Answer 7

so that means the two functions have different y-intercepts

Answer 8

now plug in another x value, say x = 1

Answer 9

f(x) = 0.001 when x = 1. g(x) = 0.001 when x = 1

Answer 10

ok try x = 2

Answer 11

I recommend making a table for x = 1, 2, 3, 4...

Answer 12

f(x) = 0.000001
g(x) = 0.002