need help with 39 - 41 .. Thanks in advance | 66.7%- ? 39. Let f()- a) (a) b) f

Question

need help with 39 - 41 .. Thanks in advance

| 66.7%- ? 39. Let f()- a) (a) b) f +1, find and smpbfy o ) 40. Based on the graph at the sight, name the basic function from the library. name its transformations, and find a possable formula for the graph 41. Find the average tate of change of foo)-+2 betwees points (x. f) and hxh)) 42. The graph fC as at the tight Approximate tbe following1I a) On what intervals is the graph increasing? b) On wbat intervals is the graph decreasing? c) On what intervals as tdhe grapl concave up? d) On what intervals is the graph cocave down? e) find the solitions of this fusction 0) If a function is even, what pr have? 43, 44. Ifa finction is odd, what property does its graph have? Wliat property doers its equation have? 45. Based on the graph at the right, a) what is the doemai? b) what is the range? c) wrste a formula for this piecewise anctson

Explanation / Answer

39) f(x) = x^2 +1

a) f(a) = a^2 +1

b) f(4/a) = (4/a)^2 +1

= 16/a^2 +1

= ( 16 + a^2)/a^2

40) transformation is on the graph of f(x) = |x|

shifted 5 units upwards

4 units to the left

reflected over x axis

f(x) = -|x +4| + 5

41) f(X) = -x^2 + 2

average rate of change = f(x+h) - f(x) / h

f(x+h) = -(x+h)^2 +2

= -(x^2 + h^2 + 2xh )

= -x^2 -h^2 - 2xh + 2

( -x^2 -h^2 - 2xh + 2 + x^2 - 2 )/ h

= (-h^2 - 2xh )/h

average rate of change = - ( h + 2x )

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