Evaluate the piecewise function when $$ x=0 $$ and $$ x=6 $$ $$ f(x)=\left\{\begin{array}{l}3 x+5 ext {, if } x \leq 5 \ \frac{1}{3} x+2 ext {, if } x5\end{array} ight. $$ The value of $$ f $$ is $$ \square $$ when $$ x=0 $$. The value of $$ f $$ is $$ \square $$ when $$ x=6 $$.

Question

Evaluate the piecewise function when $$ x=0 $$ and $$ x=6 $$ $$ f(x)=\left\{\begin{array}{l}3 x+5 	ext {, if } x \leq 5 \ \frac{1}{3} x+2 	ext {, if } x>5\end{array}ight. $$ The value of $$ f $$ is $$ \square $$ when $$ x=0 $$. The value of $$ f $$ is $$ \square $$ when $$ x=6 $$.

UpStudy AI · Accepted Answer

To evaluate the piecewise function $$ f(x) $$ at specific values of $$ x $$, we'll use the appropriate expression based on the given conditions.

The piecewise function is defined as:
$$
f(x) = \begin{cases}
3x + 5 & \text{if } x \leq 5 \
\frac{1}{3}x + 2 & \text{if } x > 5
\end{cases}
$$

### 1. Evaluating $$ f(0) $$

**Step 1:** Determine which condition $$ x = 0 $$ satisfies.

Since $$ 0 \leq 5 $$, we use the first expression:
$$
f(x) = 3x + 5
$$

**Step 2:** Substitute $$ x = 0 $$ into the expression:
$$
f(0) = 3(0) + 5 = 0 + 5 = 5
$$

**Result:**
$$
\boxed{5}
$$

### 2. Evaluating $$ f(6) $$

**Step 1:** Determine which condition $$ x = 6 $$ satisfies.

Since $$ 6 > 5 $$, we use the second expression:
$$
f(x) = \frac{1}{3}x + 2
$$

**Step 2:** Substitute $$ x = 6 $$ into the expression:
$$
f(6) = \frac{1}{3}(6) + 2 = 2 + 2 = 4
$$

**Result:**
$$
\boxed{4}
$$

### Final Answers

- The value of $$ f $$ is $$ \boxed{5} $$ when $$ x = 0 $$.
- The value of $$ f $$ is $$ \boxed{4} $$ when $$ x = 6 $$.
When $$ x = 0 $$, $$ f(x) = 5 $$. When $$ x = 6 $$, $$ f(x) = 4 $$.

Evaluate the piecewise function when \( x=0 \) and \( x=6 \) \( f(x)=\left\{\begin{array}{l}3 x+5 \text {, if } x \leq 5 \\ \frac{1}{3} x+2 \text {, if } x>5\end{array}\right. \) The value of \( f \) is \( \square \) when \( x=0 \). The value of \( f \) is \( \square \) when \( x=6 \).

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