Find the average rate of change for f(x) = x2 − 8x + 15 from x = −3 to x = 2. a) −3 b) −9 c) 3 d) 9

The rate of change between these on average is -9

Step-by-step explanation:

In order to find these, we need to evaluate the equation at both points.

x^2 - 8x + 15

-3^2 - 8(-3) + 15

9 + 24 + 15

48

This gives us the ordered pair of (-3, 48)

x^2 - 8x + 15

2^2 - 8(2) + 15

4 - 16 + 15

3

This gives us the ordered pair of (2, 3)

Now we use these two points in the slope formula to find the rate of change.

m(slope) = (y2 - y1)/(x2 - x1)

m = (48 - 3)/(-3 - 2)

m = 45/-5

m = -9

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3