Sketch a rough graph of y = x3 − 6x2 + 11x – 6.
Hint
There are three real zeros, each with multiplicity 1.
Answer
Sketch a rough graph of .
The end behavior is one arm down, on the left, and one arm up, on the right. The graph passes through at x = -1 and taps the axis at x = 3.
Sketch a rough graph of y = -x6 + 3x5 – x4 + 3x3.
Factor first; we don't actually need to use synthetic division at all.
Both arms point up. The multiplicity of the roots goes, from left to right, are odd, even, odd.
Sketch a rough graph of y = x6 + 2x5 – 9x4 – 8x3 + 14x2 – 24x + 72.
There is a root at x = 2.
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