Graph y=x^3-2

Problem

y=x3−2

Solution

1. Identify the parent function and its transformations. The function y=x3−2 is a cubic function based on the parent y=x3

2. Determine the vertical shift by looking at the constant term. The −2 indicates that the graph of y=x3 is shifted downward by 2 units.

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

y=0−2

y=−2

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

0=x3−2

x3=2

x=√(3,2)≈1.26

5. Calculate additional points to determine the shape of the curve.
   For x=1

y=1−2=−1

For x=−1

y=(−1)3−2=−3

For x=2

y=2−2=6

6. Plot the points (0,−2) (1,−1) (−1,−3) and (√(3,2),0) on a coordinate plane and draw a smooth S-shaped curve through them.

Final Answer

y=x3−2

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