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The functions f(x) and g(x) are described using the following equation and table: f(x)=4(1.02)^x
Graph in picture
Which statement best compares the y-intercepts of f(x) and g(x)?
A. The y-intercept of f(x) is equal to the y-intercept of g(x).
B. The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).
C. The y-intercept of g(x) is equal to 2 times the y intercept of g(x)
D. The y intercept of g(x) is equal to 2 plus the y intercept of f(x).

The functions fx and gx are described using the following equation and table fx4102x Graph in picture Which statement best compares the yintercepts of fx and gx class=

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Answer:

Option: D is the correct answer.

     D.  The y intercept of g(x) is equal to 2 plus the y intercept of f(x).

Step-by-step explanation:

We know that the y-intercept of a function is the y-value of the point where the x-value is zero.

i.e. it is the value of the function  where x=0.

The function f(x) is given by:

[tex]f(x)=4\times (1.02)^x[/tex]

Now, when x=0 we have:

[tex]f(0)=4\times (1.02)^0\\\\i.e.\\\\f(0)=4[/tex]

and after looking at the table of values of the function f(x) we observe that:

when x=0      g(x)=6.

This means that the y-intercept of function f(x) is : 4

and the y-intercept of the function g(x) is : 6

i.e. y-intercept of the function g(x) =2+y-intercept of function f(x)

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