Graph f(x)=x^3

Problem

ƒ(x)=x3

Solution

1. Identify the function type as a cubic function, which is an odd function because ƒ*(−x)=−ƒ(x) This means the graph is symmetric about the origin.

2. Determine the domain and range. For ƒ(x)=x3 both the domain and the range are all real numbers, (−∞,∞)

3. Calculate key points to plot. Choose a variety of x values to see the shape:

• If x=−2 ƒ*(−2)=(−2)3=−8

• If x=−1 ƒ*(−1)=(−1)3=−1

• If x=0 ƒ(0)=0=0

• If x=1 ƒ(1)=1=1

• If x=2 ƒ(2)=2=8

4. Analyze the behavior. As x→∞ ƒ(x)→∞ As x→−∞ ƒ(x)→−∞ The graph passes through the origin (0,0) which is an inflection point where the curve changes from concave down to concave up.

5. Sketch the curve by connecting the points (−2,−8) (−1,−1) (0,0) (1,1) and (2,8) with a smooth, continuous "S" shaped line.

Final Answer

To graph ƒ(x)=x3 plot the points (−2,−8),(−1,−1),(0,0),(1,1),(2,8) and draw a smooth curve through them that increases across the entire domain.

Want more problems? Check here!