Consider the function f(x)=−5x−8 and find the following: a) the average rate of change between the points (−1,f(−1)) and (3,f(3)) . b) the average rate of change between the points (a, f(a)) and (b, f(b)) . c) the average rate of change between the points (x, f(x)) and (x+h, f(x+h)) .

a. -5

b.-5

c.-5

Step-by-step explanation:

In order to find the average rate of change of a function , we divide the change in the output value by the change in the input value.

Generally, the average rate of change (ARC) on an ecuatios  between two points (x1,f(x1)) and (x2,f(x2)) is

In case a)

f(-1)= -5*(-1)-8=5-8= -3          f(3)= -5*3-8= -23

Then ARC= (-23-(-3))/(3-(-1))=-20/4=-5

In case b)

f(a)= (-5a-8)

f(b)= (-5b-8)

Then ARC= [(-5b-8)-(-5a-8)]/(b-a)= (-5b+5a)/(b-a)= -5(b-a)/(b-a)= -5

In case c)

f(x)= -5x-8

f(x+h)= -5(x+h)-8= -5x-5h-8

then ARC= [(-5x-5h-8)-(-5x-8)]/(x+h-x) =-5h/h= -5

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

345

step-by-step explanation: