(2 points) Consider the function f(x)- 2r +5 8z +3 For this function there are t
ID: 2885128 • Letter: #
Question
(2 points) Consider the function f(x)- 2r +5 8z +3 For this function there are two important intervals: (-oo, A) and (A, oo) where the function is not defined at A Find A Find the horizontal asymptote of f(x): Find the vertical asymptote of f(x): For each ot the tollowing intervals, tell whether fx)s increasing (type in INC) or decreasing type in DEC) (?,00) Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether f(x) s concave up (type in CU) or concave down (type in CD) (4,00) Sketch the graph of f(r) off lineExplanation / Answer
The function is undefined when denominator becomes 0
8x+3=0
x =-3/8
Intervals are (-inf,-3/8)U(-3/8 , inf)
Therefore A =-3/8
Horizontal asymptote
Since numerator's and denominator's degree are equal . Therefore horizontal asymptote is the ratio of there coefficient
y=2/8
y=1/4
Vertical asymptote
8x+3=0
x =-3/8
f '(x) = -34/(8x+3)2
In (-inf, -3/8) , f '(x) >0 , So its an increasing interval
In (-3/8, inf), f '(x)<0, decreasing interval
f ''(x) = 544/(8x+3)2
In (-inf, -3/8), f ''(x) <0 , concave down
In (-3/8, inf), f''(x) >0, concave up
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