Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Use the graphs and transformations of Sections 1.2 and 1.3. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = 1/2 (3x − 2),    x ≤ 3

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A: Given that: Graph of f(x)

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A: In this question we have to determine on which point f has discontinous.

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A: Please see the explanation below

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A: Any function f is continuous at 'a' if 1) f(a) is defined. 2) limx→af(x) exist. 3) limx→af(x)=f(a)

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A: We will find the answers to all the parts as following.

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A: If f'&gt;0 then f(x) will be increasing. That occurs in (6,10) If f'&lt;0 then f(x) will be…

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A: Given graph of f' is,

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A: An infinite discontinuity occurs when either one side or both side limit tends to infinity.

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

A: (1) f(x)=1x,x≥1 The graph would be, Maximum is (1,1)

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A: Option 1 is correct because as observed from the graph, maximum point is at x=a Option c is correct…

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Q: ,0< x<1 C) graph the following function f(x) = {2 – x , 1< x<2 %3D

A: The graph of the given function is shown below.

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A: It is given that a function is not defined at a   Here the graph is not defined at x=-4

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A: To sketch the graph of,  f(x) = -x3+1f(x)=x3+1f(x)=4x3+1

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A: We will use the following properties to answer this

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A: We have to draw the graph