Graph y=x^3-1

Problem

y=x3−1

Solution

1. Identify the parent function and its transformations. The function y=x3−1 is a cubic function based on the parent y=x3 shifted downward by 1 unit.

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

y=0−1

y=−1

The y-intercept is at (0,−1)

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

0=x3−1

x3=1

x=1

The x-intercept is at (1,0)

4. Determine the end behavior of the cubic function. As x→∞ y→∞ As x→−∞ y→−∞

5. Calculate additional points to refine the shape of the curve.
   If x=2 y=2−1=7
   If x=−1 y=(−1)3−1=−2
   If x=−2 y=(−2)3−1=−9

6. Sketch the graph by plotting the points (0,−1) (1,0) (2,7) (−1,−2) and (−2,−9) and connecting them with a smooth curve that passes through the inflection point at (0,−1)

Final Answer

y=x3−1

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