Graph f(x)=x^3-2

Problem

ƒ(x)=x3−2

Solution

1. Identify the parent function as y=x3 which is a cubic function with a characteristic "S" shape passing through the origin (0,0)

2. Determine the transformation by noting the constant −2 subtracted from the function, which represents a vertical shift downward by 2 units.

3. Find the y-intercept by evaluating ƒ(0)

ƒ(0)=0−2=−2

4. Find the x-intercept by setting ƒ(x)=0 and solving for x

x3−2=0

x3=2

x=√(3,2)≈1.26

5. Calculate additional points to define the curve, such as ƒ(1)=−1 ƒ(2)=6 ƒ*(−1)=−3 and ƒ*(−2)=−10

6. Plot the points and draw a smooth curve that increases across the entire domain, passing through the inflection point at (0,−2)

Final Answer

ƒ(x)=x3−2

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