See attached

if f is a function such that the quotient of the quantity f of b minus f of a and the quantity b minus a equals 2, then which of the following statements must be true?

f(a) = f(b) = 2
the slope of the tangent line to the function at x = a is 2.
the average rate of change of the function on the interval [a, b] is 2
the linear approximation for f(x) at x = a is y = 2

Step-by-step explanation:

The given expression is

Notice that and are elements of the domain and and are elements of the range.

Observe the notation used,  an element of the range is always written like where is an element of the domain.

Also, notice that this expression is using two pair of coordinates, which are and .

On the other hand, the definition of average rate of change is

Where and .

Having said that, the given expression represents an average rate of change in the interval, where the rate is 2. The right answer is the third option.

answer: (yeees, you need a poet.)

//blooming serenity//

beautiful in the morning

mysterious at night

wonderous nature souring

with all it's mystical might

the flower that blooms

to the fox that looms

nocturnal creatures

with various features

a blooming flower soon in sight

as a new little hatchling fears to take flight  

afraid to leave it's calming nest,

but dear little bird, mother knows best

as sure as there are stars in the sky,

life is not about who, where what, when or why-

it's the journey that follows

adventures we swallow

of   nature's deep wonders,

natural disasters and storm's thunders.

blooming serenity

life and nature, truly is heavenly.

-kerstien lehman

step-by-step explanation:

explanation:

remove parenthesis:

=

apply rule

=

multiply fractions:

=

=

divide:

=

mordancy.