Question

The functions f(x) and g(x) are described using the following equation and table:

f(x) = 3(1.02)^x
x g(x)
-1 -4
0 6
1 8
2 10

Which statement best compares the y-intercepts of f(x) and g(x)?

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

Answer 1

When x=0, f(0) = 3 and g(0) = 6
Then
The y-intercept of g(x) is equal to 2 times the y-intercept of f(x)

Answer 2

The y-intercept of g(x) is equal to 2 times the y-intercept of f(x)

Explanation:

The functions f(x) and g(x) are described using the following equation and table

`f(x)=3(1.02)^x`

x : -1 0 1 2

g(x) : -4 6 8 10

f(x) : 2.94 3 3.06 3.12

We need to compare the y-intercept of f(x) and g(x)

As we know the y-intercept of any function when x=0.

First we find the y-intercept of f(x) and g(x), f(0) and g(0)

y-intercept of g(x), g(0) = 6

y-intercept of f(x), f(0) = 3

6 is 2 times of 3.

Therefore, The y-intercept of g(x) is equal to 2 times the y-intercept of f(x)