1.The graphs below are all of the same shape as the graph of y = x3 . Give the equations of each:
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a.
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b.
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c.
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2. Sketch the graphs of the following functions. Plot intercepts and additional points, where needed, to get an accurate shape to your graph.
a. y = 3x3
b. y = − x3 − 2
c. y = 0.5 x3 − 1
d. y = -2x3 + 3
e. y = (x − 3)3
f. y = (x − 1)3 + 2
3. Give the equations of the following graphs in the form y =(x − a)(x − b)(x − c)
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a.
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b.
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c.
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4. Sketch the graphs of the following functions (you do not need to find coordinates of the turning points):
a. y = (x − 1)(x + 3)( x − 4)
b. y = (x + 2)(x − 2)( x + 1)
c. y = (x − 1)2(x + 3)
d. y = (4x − 1)(x − 2)(x + 1)
e. y = x (x − 2)(x + 3)
f. y = -x (3 − x)(2x − 1)
