Graph f(x)=-x^3

Problem

ƒ(x)=−x^3

Solution

1. Identify the parent function as y=x^3 which is an odd function that passes through the origin and has a "snake-like" shape increasing from left to right.

2. Apply the transformation by noting the negative sign in front of the function, which represents a reflection across the xaxis.

3. Determine key points by substituting values for x into the function ƒ(x)=−x^3

4. Calculate the point at x=−2 ƒ*(−2)=−(−2)^3=−(−8)=8

5. Calculate the point at x=−1 ƒ*(−1)=−(−1)^3=−(−1)=1

6. Calculate the point at x=0 ƒ(0)=−(0)^3=0

7. Calculate the point at x=1 ƒ(1)=−(1)^3=−1

8. Calculate the point at x=2 ƒ(2)=−(2)^3=−8

9. Plot these points (−2,8) (−1,1) (0,0) (1,−1) and (2,−8) on a coordinate plane and connect them with a smooth curve that decreases from left to right.

Final Answer

ƒ(x)=−x^3

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