The table shows the values of a function f (x), What is the average rate of change of f (x) over the interval from x = 5 to x = 9? Show your work.

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Step-by-step explanation:

1. (f(x)-f(a))/(x-a) **A(x)=(f(x)-f(a))/(x-a) This average rate of shift attribute is designated by the letter A. *f(x) - f(a) represents the difference in the function f as the input transitions from a to x. x - a represents the change in the input of the function f.

f(5)=-2 f(9)=14 (f(5)-f(9))/(5-9)=(-2-14)/-4=4 (f(5)-f(9))/(5-9)=(-2-14)/-4=4

Over the range of x = 5 to x = 9, the average rate of change is 4.

2. g(x)=2x2+13x+1, f(x)=4x2+6x

(f/g)(x)=(4x2+6x)/(2x2+13x+1) (f/g)(x)=(4x2+6x) (f/g)(x)=(4x2+6x)

f(x): 88/85,155/116,180/151,238/190,304/233,378/280 f(x): 88/85,155/116,180/151,238/190,304/233,378/280 f(x): 88/85,155/116,180/151,238/190,304/233,378/280 f(x): 88/85

3. f(x)=x2-6x+8, g(x)=x-2, g(x)=x-2, f(x)=g (x)

x2-6x+8=x-2, x2-6x-x+8+2=0, x2-7x+10=0, x2-6x-x+8+2=0

x1,2=(7+(72-4*10))/2=(7+3)/2 x1=5, x2=2 x1=5 x2=2

Step-by-step explanation:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.