Graph y=x^4

Problem

y=x4

Solution

1. Identify the function type as an even power function, which is symmetric about the y-axis because (−x)4=x4

2. Determine the vertex or minimum point by evaluating the function at x=0 which gives y=0=0

3. Calculate several points to determine the shape: when x=1 y=1 when x=−1 y=1 when x=2 y=16 and when x=−2 y=16

4. Observe the end behavior as x→∞ y→∞ and as x→−∞ y→∞

5. Sketch the curve, noting that it is flatter than a parabola (y=x2 near the origin and rises more steeply for |x|>1

Final Answer

y=x4

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