Compute and simplify the difference quotient fx h xh x o 1

Compute and simplify the difference quotient f(x + h) - ((x)/h. x o 1) f(x) = 7x^2 + 9x A) 14x^2 + 7h + 9x B) 14x + 7h + 9 C) 21x - 9h + 18 D) 14x + 0 Consider the function h as defined find functions f and g so that (f middot g) (x) = h(x). 2) h(x) = |2x+8| B) f(x) = |x|, g(x) = 2x + 8 C) ((x) = |x|, g[x] = 2x - 8 D) f(x) = -|x|, g(x) = 2x+8 Describe how the graph of the equation relate, to the graph of y - x^2. 3) f(X)=(X-8)^2+7 A) a translation 8 unit to the right and 7 units up B) a translation 8 units to the left and 7 unit down C) a translation 7 units to the right and 8 units up D) a translation 8 units to the left and 7 units up Describe the transformation and give the equation for the graph It is the graph of f(x)=|x| translated 6 units to the left, stretched vertically by a factor of 4 and translated 8 units down. The equation isy-4|x-6|+8 B) It is the graph of f(x) = |x| translated 6 units to the left shrunken vertically by a factor of 1/4 and translated 8 units down. The equation is y= 1/4|x-6|-8 C) It is the graph of f(x) = |x| translated 6 unit to the left, shrunken vertically by a factor of 1/4 and translated 8 units down. The equation is y y = 1/4 |x + 6| - 8 D) It is the graph of f(x) = |x| translated 6 units to the left, stretched vertically by a factor of 4 and translated 8 units down The equation isy=4|x+6|-8

Solution

1) [ f (x + h) – f (x) ]/ h = [7 ( x + h) ² + 9 ( x + h) – 7x² + 9x ]/ h = ( 7 x² + 14xh + 7h² + 9x + 9h – 7x² – 9x )/h

= (14xh + 7h² + 9h )/h = 14x + 7h + 9 The answer B) is correct.

2)(fog)(x) = f[ g(x)] ; h(x) = ( 2x + 8);Now if f (x) = x and g (x) = 2x + 8, then (fog)(x) = f[ g(x)] = f ( 2x +8) = 2x + 8 = h (x). Thus, answer A) is correct.

3)    f (x) = ( x - 8)² + 7 is a translation of the graph of y = x²   , 8 units to the right and 7 units up. Thus, answer A) is correct ( the vertex of the parabola shifts from ( 0, 0) to ( 8,7) )

4) The answer C) is correct. It is the graph of f (x) = mod (x) translated 6 units to the left, shrunken vertically by a factor of ¼ and translated 8 units down. Its equation is y = ¼ mod ( x + 6) - 8 ( we can prepare the graphs of the two functions, using a graphing calculator and compare )