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(b)
6

(b) $\newline$ $6$

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Evaluate piecewise-defined functions

Full solution

Q. (b)

\newline

6

Use first part of function: Since $-9$ is less than $3$ , we use the first part of the piecewise function: $f(x) = \frac{1}{3}x + 6$ .
Substitute $-9$ for $x$ : Substitute $-9$ for $x$ : $f(-9) = \frac{1}{3} \times (-9) + 6$ .
Perform multiplication: Perform the multiplication: $\frac{1}{3} \times (-9) = -3$ .
Add $6$ to $-3$ : Add $6$ to $-3$ : $f(-9) = -3 + 6$ .
Calculate the sum: Calculate the sum: $f(-9) = 3$ .

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