Consider the function f(x)=x−2x+3
.



(a) Find the domain of f(x)
.



Note: Use the letter U for union. To enter ∞
, type infinity.



Domain:
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(b) Give the horizontal and vertical asymptotes of f(x)
, if any.



Enter the equations for the asymptotes. If there is no horizontal or vertical asymptote, enter NA in the associated response area.



horizontal asymptote:
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vertical asymptote:
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(c) Give the intervals of increase and decrease of f(x)
.



Note: Use the letter U for union. To enter ∞
, type infinity.

If the function is never increasing or decreasing, enter NA in the associated response area.



increasing:
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decreasing:
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(d) Give the local maximum and minimum values of f(x)
.



Enter your answers in increasing order of the x
-value. If there are less than two local extrema, enter NA in the remaining response areas and the corresponding drop-down menu.



Include a multiplication sign between symbols. For example, a⋅π
.



f(

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f(

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(e) Give the intervals of concavity of f(x)
.



Note: Use the letter U for union. To enter ∞
, type infinity.

If the function is never concave upward or concave downward, enter NA in the associated response area.



concave upward:
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concave downward:
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(f) Give the inflection points of f(x)
.



Enter your answers in increasing order of the x
-coordinate. If there are less than two points of inflection, enter NA in the remaining response areas.



Include a multiplication sign between symbols. For example, a⋅π
.