Graph y=x^5

Problem

y=x5

Solution

1. Identify the function type as an odd-degree power function. Since the exponent 5 is odd, the graph will have origin symmetry, meaning ƒ*(−x)=−ƒ(x)

2. Determine the end behavior of the function. As x→∞ y→∞ As x→−∞ y→−∞

3. Find the intercepts by setting x=0 and y=0 The graph passes through the origin (0,0) which is both the x-intercept and the y-intercept.

4. Analyze the shape near the origin. Because the power is higher than 1 the graph is flatter than y=x3 near x=0 and steeper for |x|>1

5. Plot key points to define the curve.

(−2,−32)

(−1,−1)

(0,0)

(1,1)

(2,32)

6. Sketch the curve by connecting the points with a smooth, continuous line that passes through the origin with a horizontal tangent.

Final Answer

y=x5

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