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.)
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.)
Solution
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 \( \boxed{3} \)