Question

The functions f(x) and g(x) are described using the following equation and table: f(x) = −6(1.05)x x g(x) −4 −9 −2 −6 0 −3 2 2 Which equation best compares the y-intercepts of f(x) and g(x)?

Answer 1

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

Answer 2

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

Explanation:

we know that

The y-intercept is the value of the function when the value of x is equal to zero

step 1

Find the y-intercept of f(x)

we have

`f(x)=-6(1.05)^(x)`

For x=0

`f(0)=-6(1.05)^(0)`

`f(0)=-6(1)`

`f(0)=-6`

The y-intercept is the point (0,-6)

step 2

Find the y-intercept of g(x)

Observing the table

For x=0

`g(0)=-3`

The y-intercept is the point (0,-3)

step 3

Compare the y-intercepts

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