Question

Please help! ASAP! Thanks!

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)?

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 1

(A) is your answer. The graph of g(x) will eventually exceed the graph of f(x).

Answer 2

A. The graph of g(x) will eventually exceed the graph of f(x).

Explanation:

We are given the functions,

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

Now, 'y-intercepts are the points where the graph cuts y-axis i.e. where x= 0'.

So, substituting x= 0, we get,

`f(0)=0.001^0` i.e. f(0) = 1

`g(0)=0.001* 0` i.e. g(0 )= 0

That is, the function f(x) have y-intercept at 1 and the function g(x) have y-intercept at 0.

So,options C and D are not correct.

We have the table,

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

1 0.001 0.001

2 0.00001 0.002

3 0.000000001 0.003

4 0.000000000001 0.004

So, we get that the fucntion g(x) is increasing as the value of x is increasing as compared to f(x)/

Hence, the graph of g(x) will eventually exceed the graph of f(x).

So, option A is correct.