Evaluate the piecewise function at the given values of the independent variable. $$ f(x)=\left\{\begin{array}{ll}5 x+4 & ext { if } x

Question

Evaluate the piecewise function at the given values of the independent variable. $$ f(x)=\left\{\begin{array}{ll}5 x+4 & 	ext { if } x<0 \ 2 x+5 & 	ext { if } x \geq 0\end{array}ight. $$ (a) $$ f(-1) $$ (b) $$ f(0) $$ (c) $$ f(2) $$

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Let's evaluate the piecewise function $$ f(x) $$ at the specified values of $$ x $$:

$$
f(x) = \begin{cases} 
5x + 4 & \text{if } x < 0 \
2x + 5 & \text{if } x \geq 0 
\end{cases}
$$

### (a) $$ f(-1) $$

**Step 1:** Determine which part of the piecewise function to use.

Since $$ -1 < 0 $$, we use:
$$
f(x) = 5x + 4
$$

**Step 2:** Substitute $$ x = -1 $$ into the function.
$$
f(-1) = 5(-1) + 4 = -5 + 4 = -1
$$

**Answer:** $$ f(-1) = -1 $$

---

### (b) $$ f(0) $$

**Step 1:** Determine which part of the piecewise function to use.

Since $$ 0 \geq 0 $$, we use:
$$
f(x) = 2x + 5
$$

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

**Answer:** $$ f(0) = 5 $$

---

### (c) $$ f(2) $$

**Step 1:** Determine which part of the piecewise function to use.

Since $$ 2 \geq 0 $$, we use:
$$
f(x) = 2x + 5
$$

**Step 2:** Substitute $$ x = 2 $$ into the function.
$$
f(2) = 2(2) + 5 = 4 + 5 = 9
$$

**Answer:** $$ f(2) = 9 $$

---

**Summary of Results:**
- **(a)** $$ f(-1) = -1 $$
- **(b)** $$ f(0) = 5 $$
- **(c)** $$ f(2) = 9 $$
$$ f(-1) = -1 $$, $$ f(0) = 5 $$, $$ f(2) = 9 $$.

Evaluate the piecewise function at the given values of the independent variable. \( f(x)=\left\{\begin{array}{ll}5 x+4 & \text { if } x<0 \\ 2 x+5 & \text { if } x \geq 0\end{array}\right. \) (a) \( f(-1) \) (b) \( f(0) \) (c) \( f(2) \)

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