True/False 1) The graph of a function f(x) cannot intersect its vertical asympto

Question

True/False 1) The graph of a function f(x) cannot intersect its vertical asymptote. 2) The graph of a function f(x) cannot intersect its horizontal asymptote. 3) Iff(x) is not continuous on the interval [a,b] then f(x) cannot have an absolute maximum value. 4) Iff(x) is defined on a closed interval [a,b] then f(x) has an absolute minimum value. 5) If f(x) is continuous on [a,b], f(x) is differentiable on (a,b), and f (x) + 0 for all x in (a,b), then the absolute maximum value of f(x) on [a,b] is f(a) or f(b) 6) Ifx 0 and x>o. 9) f(x)- e is an increasing function if k>0 and a decreasing function if k0 and b>0 then ln(a+b)=In a +1nb 12) If b> 0 ,then e -lne 13) If f(x) = 3x thenf,(x)-x3-1 14) If f(x)-e" thenf'(x)-e" 15) If f (x)-rx then f '(x) = 16) If f(x)=e3x, thenf,(x)=e6x 17) f(x)-Inlxl thenf,(x)- 18) f(x) In 5 thenf'(x) 19) f(x)=ln(x +5)2 thenf,(x)= 20) If you are modeling exponential decay, you can use a model of the form (t)Qe*" x +

Explanation / Answer

1) True, it can't intersect the vertical asymptote, by definition of asymptote. The vertical asymptote indicates that it goes to infinity as it gets closer to a certain point x_0 . f(x) is not defined in x_0 therefore it can't touch the asymptote.

2) False , If it were a horizontal or oblique asymptote, it could intersect it before it tends to infinity.

3) True, a continuous function that is defined on a closed interval must have both an absolute maximum value and an absolute minimum value

4) True, a continuous function that is defined on a closed interval must have both an absolute maximum value and an absolute minimum value

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