need help for my algebra class 14. Find tde rate of chunge over the interval fom

Question

need help for my algebra class

14. Find tde rate of chunge over the interval fom D.3. O:-2 O: 2 O:-1 15. Find the value of k, such that ie+x+ 4 will leave a remainder of 4 when divided O: 4 O:3 0:-3 16, Given f(x)-om(x+3) and g(x)-3, find the x valne such that f(x)-g(x) O: Gl 0:22 17. Select the graph with the same zeros as the function foc)-4X6x+3) O: O: O: O: 18, The graphs off(x)-log 9(?-4) + 2 and g(x)-9-4 + 2 would have the same asymptotes located at 0: x = 4, y-2 and respectively 19. Calculate the average rate of change of the graph over the interval from [1,3). o:-I 0:-2 0:2 Turn to the next page

Explanation / Answer

14) We see that f(1) = 6 and f(3) = 4
So rate of change = derivative = slope = y2-y1 / x2-x1 = (4-6) / (3-1) = -22 = -1
Thus,rate of change = -1

15) We know that a function f(x) when divided by (x-a) will have the remainder of f(a)
Thus, f(x) = x3 - 4x2 + kx + 4;
When divided by (x-1) , it's remainder = f(1) (as per remainder theorem)
Thus, f(1) = 4 as per the question
f(1) = 13 - 4(1)2 + k(1) + 4 = 1-4 + k + 4 = k+1
k+1 = 4 then k=4-1 = 3;
Thus, f(x) = x3 - 4x2 + 3x + 4 and k=3
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