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Question
Draw the graph of the following function:
f(x) = x |x|
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Solution
Let y = f(x) = x|x|
f(x) = `{(x(x) if x >= 0),(x(-x) if x < 0):}`
f(x) = `{(x^2 if x >= 0),(- x^2 if x < 0):}`
y = x2, x ≥ 0
| x | 0 | 1 | 2 | 3 |
| y | 0 | 1 | 4 | 9 |
y = -x2, x < 0
| x | -1 | -2 | -3 |
| y | -1 | -4 | -9 |
Plot the points (0, 0), (1, 1) (2, 4), (3, 9), (-1, -1), (-2, -4), (-3, -9) and draw a smooth curve.
The graph is as shown in the figure.
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