Question:

Help with calc homework?

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f(x)= -1 if x <=(less than or equal to) -1

3x+2 if |x| <1

7-2x if x >= 1

I already have the domains (at lease I think so... (-1,-1)(0,0) (1,infinity)) and I cant remember how to graph...help?

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  1. f(x) is defined for any real number ==&gt; Domain=R

    Graph:

    http://i299.photobucket.com/albums/mm286...

    x≤-1 ==&gt; y= -1

    The graph is a half-line parallel to the x-axis with starting point at (-1,-1)

    and heading left.

    -1&lt;x&lt;1 ==&gt; y=3x+2

    x=-1 ==&gt; y=-1

    x=1 ==&gt; y=5

    The graph is a line segment obtained by connecting the points (-1,-1) and (1,5). As x approaches -1, the graph tends to (-1,-1). As x approaches 1, the graph tends to (1,5).

    x≥1 ==&gt; y=7-2x

    x=1 ==&gt; y=5

    x=2 ==&gt; y=3

    The graph is a half-line starting at (1,5) and  passing through (2,3).


  2. I&#039;m not sure about the domains you have listed there... I believe they are:

    (-infinity, -1]

    (-1,1)

    [1, infinity)

    Just find the value of the function f(x) at each of the endpoints (except -infinity and infinity) and connect the dots.  It&#039;s a stepwise continuous function meaning that there are no sudden jumps through thin air - the lines all connect with each other.  Since you can&#039;t get a numerical value for the function at -infinity and infinity, instead just try numbers like -5 and 5 so that you have some points you can draw the line through.

    Hope this helps, let me know if you need any clarifications.  

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