Graph y=x^3+1

Problem

y=x3+1

Solution

1. Identify the parent function and the transformation. The parent function is y=x3 which is a cubic function with an S-shape passing through the origin (0,0)

2. Determine the vertical shift by looking at the constant term. The +1 indicates that the entire graph of y=x3 is shifted upward by 1 unit.

3. Find the y-intercept by setting x=0

y=0+1

y=1

The y-intercept is at (0,1)
4. Find the x-intercept by setting y=0

0=x3+1

x3=−1

x=−1

The x-intercept is at (−1,0)
5. Calculate additional points to determine the shape.
If x=1 y=1+1=2
If x=−2 y=(−2)3+1=−7
6. Sketch the curve through the points (−2,−7) (−1,0) (0,1) and (1,2) ensuring the graph shows the characteristic cubic "inflection point" at (0,1)

Final Answer

y=x3+1

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