2x +5 6x +5 (2 pts) Consider the function f(x) For this function there are two i

Question

2x +5 6x +5 (2 pts) Consider the function f(x) 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 ot f(ax) For each of the folowing intervals, tell whether fx) is increasing (type in INC) or decreasing (type in DEC) (-00,A* Note that this function has no inflection points, but we can still consider its concavity. For each of the to whether f(x) is concave up (type in CU) or concave down (type in CD) lowing intervalis, tell Sketch the graph of f(x) off line.

Explanation / Answer

Horizontal asymptote

Since numerator and denominator's degree are equal. So horizontal asymptote is the ratio of numerator's leading coefficient and denominator's leading coefficient .

y=2/6=1/3

Vertical asymptote

6x+5=0

x=-5/6

Critical point, x=-5/6

In (-inf,-5/6), f '(x) is negative

In (-5/6, inf), f '(x) f'(x) is negative

So decreasing interval (-inf, -5/6)U(-5/6,inf)

Inflection point

No inflection point

in (-inf,-5/6), f ''(x)<0, so concave down

In (5/6, inf), f ''(x)>0, so concave up .

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