Question

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

f(x) = −2(1.07)x

Which equation 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 correct answer is D

Answer 2

The equation y = -2(1.07)x represents the function f(x). The y-intercept of f(x) is -2. The equation that best compares the y-intercepts of f(x) and g(x) is: A. The y-intercept of f(x) is equal to the y-intercept of g(x).

The correct answer to the given question is option A.

The equation y = -2(1.07)x represents the function f(x). To compare the y-intercepts of f(x) and another function, we can substitute x = 0 into the equation and calculate the corresponding value of y.

Substituting x = 0 into the equation y = -2(1.07)x gives us y = -2(1.07)0 = -2(1) = -2.

The y-intercept of f(x) is -2.

Comparing this with the table for g(x), we can see that the y-intercept of g(x) is also -2.

Therefore, the equation that best compares the y-intercepts of f(x) and g(x) is: A. The y-intercept of f(x) is equal to the y-intercept of g(x).