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b)
DE

b) $\mathrm{DE}$

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Evaluate piecewise-defined functions

Full solution

Q. b)

\mathrm{DE}

Identify Part for $x = -9$ : Identify which part of the piecewise function to use for $x = -9$ . $\newline$ Since $-9$ is less than $3$ , we use the first part of the function: $f(x) = \frac{1}{3}x + 6$ .
Substitute $x$ in $f(x)$ : Substitute $x$ with $-9$ in the function $f(x) = \frac{1}{3}x + 6$ . $\newline$ $f(-9) = \frac{1}{3} \times (-9) + 6$ .
Perform Multiplication: Perform the multiplication $\frac{1}{3} \times (-9)$ . $\newline$ $f(-9) = -3 + 6$ .
Add to Find $f(-9)$ : Add $-3$ to $6$ to find the value of $f(-9)$ . $\newline$ $f(-9) = 3$ .

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