Question

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

f(x) = 4(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)?
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 f(x).
D.The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).

Answer 1

The y-intercept is the value of the function for x = 0.

Then, the y-intercept of f(x) = 4(1.02)^x is 4 (1.02)^0 = 4(1) = 4

And the y intercept of g(x) is read on the table. x = 0 => g(x) = 6.

So, you can see that g(x) = 6 = 4 + 2 = y-intercept of f(x) plus 2.

Answer: option D. the y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).