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Sketch the graph for
Solution:
The first thing that we have to do is to factor the given equation by synthetic division as follows
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| Photo by Math Principles in Everyday Life |
The x-intercepts are -1, 1, 2, and 3. To get the y-intercept, set x = 0 to the given equation, we have
Now, plot the points -1, 1, 2, and 3 along the x-axis and 6 along the y-axis. These points will pass the curve. To get the direction of the curve, let's consider the following
if x < 3, then y = (-)(-)(-)(-) = (+)
- 3 < x < -1, then y = (-)(-)(+)(-) = (-)
-1 < x < 1, then y = (+)(-)(+)(-) = (+)
1 < x < 2, then y = (+)(-)(+)(+) = (-)
x > 2, then y = (+)(+)(+)(+) = (+)
Connect all the points and the graph must be like this
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| Photo by Math Principles in Everyday Life |