Graph y=x^3+2

Problem

y=x3+2

Solution

1. Identify the parent function as y=x3 which is a cubic function with a characteristic "S" shape passing through the origin (0,0)

2. Determine the vertical shift by observing the constant +2 added to the parent function.

3. Apply the transformation by shifting every point on the graph of y=x3 upward by 2 units.

4. Calculate key points to plot the curve:

• If x=−2 y=(−2)3+2=−6

• If x=−1 y=(−1)3+2=1

• If x=0 y=(0)3+2=2 (the y-intercept)

• If x=1 y=(1)3+2=3

• If x=2 y=(2)3+2=10

5. Sketch a smooth curve through the points (−2,−6) (−1,1) (0,2) (1,3) and (2,10) noting the inflection point at (0,2)

Final Answer

y=x3+2

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