TERRI F.

asked • 02/26/17

How do I solve and graph this problem?

Question: Draw a continuous function f that has the following characteristics, then state the zeroes and the
location of all maximum and minimum values.
(a) Domain: x ∈ (−10, ∞)
(b) Range: y ∈ (−6, ∞)
(c) f(0) = f(4) = 0
(d) f(x) is increasing for x ∈ (−10 − 6) ∪ (−2, 2) ∪ (4, ∞)
(e) f(x) is decreasing for x ∈ (−6, −2) ∪ (2, 4)
(f) f(x) ≥ 0 for x ∈ [−8, −4] ∪ [0, ∞)
(g) f(x) < 0 for x ∈ (−10, −8) ∪ (−4, 0)

1 Expert Answer

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Michael J. answered • 02/26/17

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Mathematical Reasoning and Logic Application

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I already answered this question for you several days ago.  Did you even read the solution I provided?
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TERRI F.

Yes sir. I am confused on the graphing part. My open circle looks more like a wavy line. Just trying to make sure 
I am understanding this right. 
Your answer:
Starting at x=-10, draw an open circle at the (-10,-6). The curve increases from that point to x=6. It crosses the x-axis at x=-8 during this increase. Then, from x=6, decreases to x=-2. It crosses the x-axis at x=-4 during this decrease. From x=-2, the curve starts to increase a second time to x=2. It crosses the x-axis at x=0 during this second increase. From x=2, the curve decreases to x=4. It touches the x-axis at x=4 during this second decrease. Then, from x=4, it increases without any end.
I can't seem to interpret the answer you gave into a graph I'm confused. 



Here is a summary of the crucial points

x-intercepts: (-8, 0) , (-4, 0) , (0, 0) , (4, 0)

Maximum values: x=-6 and x=-2
Minimum values: x=-2 and x=4

Intervals below the x-axis: (-10, -8)∪(-4, 0)
Intervals above the x-axis: (-8, -4)∪(0, 4)∪(4, ∞)Starting point (open circle) at (-10, -6).
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02/26/17

Michael J.

It increases from x=-10 to x=-6.  Then from that point, it starts to decrease until the next interval of increase.  The next increase is in the interval (-2, 2).  That means the interval between the intervals of increase is where the graph decrease.  x=-6 is where your first maximum takes place.  Since you have 3 intervals of increase and 2 intervals of decrease, the graph increases 3 times.  The graph decreases 2 times.  Do you get the idea?  Can you picture it better? 
 
Just take it one step at a time.  Draw the graph piece by piece.
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02/26/17

Michael J.

Also, your second maximum takes place at x=2.  Not      x = -2
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02/26/17

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