G(t)= -(t-1)^2 +5g(t)=−(t−1) 2 +5g, (, t, ), equals, minus, (, t, minus, 1, ), squared, plus, 5 What is the average rate of change of ggg over the interval -4\leq t\leq 5−4≤t≤5minus, 4, is less than or equal to, t, is less than or equal to, 5?

Average rate of change is 1.

Step-by-step explanation:

The average rate of change of function over the intervals is given by the formula,

.

Rewriting the formula according to given data,

.

Given the interval as . Hence value of a and b is a = -4 and b = 5.

Now calculate and as follows.

Calculation for ,

Replace t as a,

Substituting the value,

Calculation for ,

Substituting the value,

Now substituting the value,

.

Simplifying,

.

.

.

Hence average rate of change of the given function over the given interval is 1.

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

add 8+12 to get a simplified answer of 12r-20