Question

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).

Answer 1

Option: D is the correct answer.

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

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:

`f(x)=4* (1.02)^x`

Now, when x=0 we have:

`f(0)=4* (1.02)^0\\\\i.e.\\\\f(0)=4`

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)