Question

1. The table shows values of a function . What is the average rate of change of over the interval from x = 5 to x = 9? Show your work.
x: 4 5 6 7 8 9 10



f(x): -4 -2 8 10 11 14 18

2. Given f(x)=4x^2 +6x and g(x)=2x^2+13x+1, find (f/g)(x) . Show your work.

3.Given f(x)= x^2-6x+8 and g(x)= x-2, solve f(x)=g(x) using a table of values. Show your work.

Answer 1

1. **A(x)=(f(x)-f(a))/(x-a)
*A is the name of this average rate of change function
*x - a represents the change in the input of the function f
*f(x) - f(a) represents the change in the function f as the input changes from a to x
From table: f(5)=-2
                   f(9)=14
(f(5)-f(9))/(5-9)=(-2-14)/-4=4
The average rate of change of over the interval from x = 5 to x = 9 is 4.

2. f(x)=4x²+6x, g(x)=2x²+13x+1
(f/g)(x)=(4x²+6x)/(2x²+13x+1)
Using the table of values- x:4,5,6,7,8,9
                                    f(x): 88/85,155/116,180/151,238/190,304/233,378/280

3. f(x)=x²-6x+8, g(x)=x-2
f(x)=g(x)⇒x²-6x+8=x-2⇒x²-6x-x+8+2=0, x²-7x+10=0
x₁,₂=(7⁺₋√(7²-4*10))/2=(7⁺₋3)/2
x₁=5, x₂=2
Using the table of values solution is x=5 because  2 doesn't exist in the table of values.