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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)?

AThe graph of g(x) will eventually exceed the graph of f(x).
BThe graph of f(x) will eventually exceed the graph of g(x).
CThe graphs will both have their y-intercept equal to 1.
DThe graphs will both have their y-intercept equal to 0.001.

Verified Answer :

royalgabbana1

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

Answer:

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

Step-by-step 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

\(g(0)=0.001\times 0\) 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.

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