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 −5
0 −3
1 −1
2 1

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 the y-intercept of f(x).

Answer 1

The correct answer is A, the y-intercept of f(x) is equal to the y-intercept of g(x).

Explanation:

First, note that the y intercept is what y is equal to when x is equal to 0.

The given function, f(x), is an exponential function. Exponential functions are written in the formula
`f(x) = a(1 + r)^x`, where a = y-intercept!

a in the function f(x) is -3, so this means that the y intercept is -3.

In the given table, g(x), the y value is -3 when the x value is 0.

This means that in the g(x) table, the y-intercept is also -3.

Thus, A is correct and the y-intercept of f(x) is equal to the y-intercept of g(x).

Answer 2

The y-intercept of a function is the point where the graph of the function intersects the y-axis. To find the y-intercept of f(x), we can substitute x=0 into the equation for f(x):

f(0) = -3(1.02)^0 = -3

Therefore, the y-intercept of f(x) is -3. To find the y-intercept of g(x), we can look at the table and see that when x=0, g(x)=-3. Therefore, the y-intercept of g(x) is also -3.

Comparing the y-intercepts of the two functions, we see that they are equal. Therefore, the correct answer is:

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

Explanation: