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 10f(x): -4 -2 8 10 11 14 182. 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.
Accepted Solution
A:
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.