Graph x^3

Problem

ƒ(x)=x3

Solution

1. Identify the function as a cubic parent function, which is an odd function that is symmetric about the origin.

2. Determine the domain and range, which are both all real numbers, (−∞,∞)

3. Calculate key points to plot by substituting x values into the function:

ƒ*(−2)=(−2)3=−8

ƒ*(−1)=(−1)3=−1

ƒ(0)=0=0

ƒ(1)=1=1

ƒ(2)=2=8

4. Analyze the behavior of the graph, noting that it increases across the entire domain and has a point of inflection at (0,0) where the curvature changes.

5. Sketch the curve through the points (−2,−8) (−1,−1) (0,0) (1,1) and (2,8) ensuring the graph passes through the origin and extends to infinity in both directions.

Final Answer

ƒ(x)=x3

Want more problems? Check here!