Graph cube root of x

Problem

ƒ(x)=√(3,x)

Solution

1. Identify the parent function as the cube root function, which is defined for all real numbers x because the cube root of a negative number is real.

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

3. Calculate key points to plot the curve:

• For x=−8 ƒ*(−8)=−2

• For x=−1 ƒ*(−1)=−1

• For x=0 ƒ(0)=0

• For x=1 ƒ(1)=1

• For x=8 ƒ(8)=2

4. Observe the symmetry of the function, noting that it is an odd function since ƒ*(−x)=−ƒ(x) meaning it is symmetric about the origin.

5. Sketch the graph by connecting the points with a smooth curve that is steep near the origin and flattens out as |x| increases.

Final Answer

ƒ(x)=√(3,x)

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