Graph x^4

Problem

y=x4

Solution

1. Identify the function as an even power function, which means it is symmetric about the yaxis because (−x)4=x4

2. Determine the vertex and intercepts by substituting x=0 which gives y=0 so the graph passes through the origin (0,0)

3. Analyze the end behavior: as x approaches positive or negative infinity, y approaches positive infinity.

4. Calculate key points to determine the shape: for x=1 y=1 for x=−1 y=1 for x=2 y=16 for x=−2 y=16

5. Compare the shape to a parabola y=x2 the graph of y=x4 is flatter near the origin (between x=−1 and x=1 and steeper for |x|>1

6. Sketch a U-shaped curve opening upwards, passing through (−2,16) (−1,1) (0,0) (1,1) and (2,16)

Final Answer

y=x4

Want more problems? Check here!