The table shows the values of a function f(x). what is the average rate of change of f(x) from 1 to 4?

x f(x)
0 500
1 484
2 436
3 356
4 244
5 100

-80

Step-by-step explanation:

The average rate of change is

a.r.c = f(4) - f(1)

             4-1

f(4) = 244 and f(1) = 484

a.r.c = 244  - 484

             3

        = -240/3

      =-80

The average rate of change of f(x) from 1 to 4 is -80.

Step-by-step explanation:

The average rate of change of f(x) from a to b is defined as

The average rate of change of f(x) from 1 to 4 is defined as

From the given table it is clear that the the value of the function is 244 at x=4 and 484 at x=1. So f(4)=244 and f(1)=484. Put these values in the above equation.

Therefore the average rate of change of f(x) from 1 to 4 is -80.

the second option

step-by-step explanation:

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)