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Given f(x)=3x 1 when x <0;x² when 04, evaluate f(3)

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Final answer:

Evaluate f(3) by using the correct piece of the piecewise function, which is f(x) = x² for x ≥ 0. Thus, f(3) = 3² = 9.

Step-by-step explanation:

To evaluate f(3), we need to look at the function f(x) and determine which part of the piecewise function applies to

x = 3.

Based on the given information, we have two expressions for f(x): f(x) = 3x + 1 when x < 0, and f(x) = x² when x ≥ 0. Since 3 is greater than 0, we use the second expression.

So f(3) = 3² = 9. The positive value and positive decreasing slope at x = 3 suggest that a parabolic function like y = x² is a better fit than a linear function like y = 13x, which would have a constant slope, not a decreasing one.

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