Evaluate the piecewise function at the given values of the independent variable.

(a)

Ask by Pierce Stewart. in the United States

Mar 23,2025

Question

Evaluate the piecewise function at the given values of the independent variable. $$ f(x)=\left\{\begin{array}{ll}4 x+3 & 	ext { if } x<0 \ 2 x+7 & 	ext { if } x \geq 0\end{array}ight. $$ $$ \begin{array}{l}	ext { (a) } f(-4) \ 	ext { (b) } f(0) \ 	ext { (c) } f(4)\end{array} $$ (a) $$ f(-4)=\square $$

UpStudy AI · Accepted Answer

**Step 1:** Identify the correct piece of the function.  
Since $$-4 < 0$$, we use the definition $$ f(x) = 4x + 3 $$.

**Step 2:** Substitute $$ x = -4 $$ into the expression:  
$$
f(-4) = 4(-4) + 3
$$

**Step 3:** Compute the multiplication:  
$$
4(-4) = -16
$$

**Step 4:** Add 3 to the product:  
$$
-16 + 3 = -13
$$

Thus,  
$$
f(-4) = -13
$$
$$ f(-4) = -13 $$

Evaluate the piecewise function at the given values of the independent variable.

(a)

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Evaluate the piecewise function at the given values of the independent variable. (a)