Question

Find the net change in the value of the function between the given inputs.

g(t) = 2 − t2; from −3 to 7

Answer 1

The net change in the value of the function g(t) = 2 - t^2 from -3 to 7 is -40.

Step-by-step explanation:

To find the net change in the value of the function from -3 to 7, we need to subtract the value of the function at the initial point from the value at the final point.

Substituting -3 into the function g(t) = 2 - t^2, we get g(-3) = 2 - (-3)^2 = 2 - 9 = -7.

Substituting 7 into the function, we get g(7) = 2 - (7)^2 = 2 - 49 = -47.

Therefore, the net change in the value of the function from -3 to 7 is -47 - (-7) = -40.

Answer 2

`-54`

Step-by-step explanation:

The net change of
`g(t)` from
`-3` to
`7` is just
`g(7) -g(-3)`.

Given:

`g(t) = 2 -t^2`

Solution:

`g(7) -g(-3) \\ (2 -(7)^2) -(2 -(-3)^2) \\ (2 -49) -(2 -9) \\ -47 -7 \\ -54`