Questions: For the linear function f(x)=(3-x)/6; (a) evaluate f(-3) and f(6); (b) find the zero of f, a (a) f(-3)=1 (Type an integer or a simplified fraction.) f(6)=-1/2 (Type an integer or a simplified fraction.) (b) The zero of f is (Type an integer or a simplified fraction.)

For the linear function f(x)=(3-x)/6; (a) evaluate f(-3) and f(6); (b) find the zero of f, a
(a) f(-3)=1 (Type an integer or a simplified fraction.)
f(6)=-1/2 (Type an integer or a simplified fraction.)
(b) The zero of f is (Type an integer or a simplified fraction.)
Transcript text: For the linear function $f(x)=\frac{3-x}{6} ;$ (a) evaluate $f(-3)$ and $f(6)$; (b) find the zero of $f$, $a$ (a) $f(-3)=1$ (Type an integer or a simplified fraction.) $f(6)=-\frac{1}{2}$ (Type an integer or a simplified fraction.) (b) The zero of $f$ is $\square$ (Type an integer or a simplified fraction.)
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Solution

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Solution Steps

Step 1: Evaluate \( f(-3) \)

Substitute \( x = -3 \) into the function \( f(x) = \frac{3 - x}{6} \): \[ f(-3) = \frac{3 - (-3)}{6} = \frac{6}{6} = 1 \]

Step 2: Evaluate \( f(6) \)

Substitute \( x = 6 \) into the function \( f(x) = \frac{3 - x}{6} \): \[ f(6) = \frac{3 - 6}{6} = \frac{-3}{6} = -\frac{1}{2} \]

Step 3: Find the zero of \( f \)

To find the zero of \( f \), set \( f(x) = 0 \) and solve for \( x \): \[ \frac{3 - x}{6} = 0 \] Multiply both sides by 6: \[ 3 - x = 0 \] Solve for \( x \): \[ x = 3 \]

Final Answer

(a) \( f(-3) = \boxed{1} \)
\( f(6) = \boxed{-\frac{1}{2}} \)
(b) The zero of \( f \) is \( \boxed{3} \)

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