Graph y=x^3

Problem

y=x3

Solution

1. Identify the function type as a cubic function, which is an odd function that is symmetric about the origin.

2. Determine the domain and range, which are both all real numbers, (−∞,∞)

3. Calculate key points to plot by substituting values for x

• If x=−2 y=(−2)3=−8

• If x=−1 y=(−1)3=−1

• If x=0 y=0=0

• If x=1 y=1=1

• If x=2 y=2=8

4. Analyze the behavior as x increases; the function increases across its entire domain, with a horizontal tangent (inflection point) at the origin (0,0)

5. Sketch the curve through the points (−2,−8) (−1,−1) (0,0) (1,1) and (2,8) ensuring the graph curves upward for x>0 and downward for x<0

Final Answer

y=x3

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