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

Ask by Mcdonald Wade. in the United States

Mar 23,2025

Question

Evaluate the piecewise function at the given values of the independent variable. $$ f(x)=\left\{\begin{array}{ll}4 x+3 & 	ext { if } x<0 \ 2 x+7 & 	ext { if } x \geq 0\end{array}ight. $$ $$ \begin{array}{l}	ext { (a) } f(-4) \ 	ext { (b) } f(0) \ 	ext { (c) } f(4) \ 	ext { (a) } f(-4)=-13 \ 	ext { (b) } f(0)=\square\end{array} $$

UpStudy AI · Accepted Answer

To evaluate the piecewise function $$ f(x) $$, we will consider each case based on the value of $$ x $$.

The function is defined as:
$$
f(x) = 
\begin{cases} 
4x + 3 & \text{if } x < 0 \ 
2x + 7 & \text{if } x \geq 0 
\end{cases}
$$

Now, let's evaluate the function at the specified values:

### (a) $$ f(-4) $$
Since $$-4 < 0$$, we use the first case of the piecewise function:
$$
f(-4) = 4(-4) + 3
$$

### (b) $$ f(0) $$
Since $$0 \geq 0$$, we use the second case of the piecewise function:
$$
f(0) = 2(0) + 7
$$

### (c) $$ f(4) $$
Since $$4 \geq 0$$, we again use the second case of the piecewise function:
$$
f(4) = 2(4) + 7
$$

Now, let's perform the calculations for each case.
Calculate the value by following steps:
- step0: Calculate:
  $$2\times 0+7$$
- step1: Multiply:
  $$0+7$$
- step2: Remove 0:
  $$7$$
Calculate or simplify the expression $$ 4*(-4) + 3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$4\left(-4\right)+3$$
- step1: Multiply the numbers:
  $$-16+3$$
- step2: Add the numbers:
  $$-13$$
Calculate or simplify the expression $$ 2*(4) + 7 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$2\times 4+7$$
- step1: Multiply the numbers:
  $$8+7$$
- step2: Add the numbers:
  $$15$$
Now, let's summarize the evaluations:

### Results:
- (a) $$ f(-4) = -13 $$
- (b) $$ f(0) = 7 $$
- (c) $$ f(4) = 15 $$

Thus, the completed evaluations are:
- $$ f(-4) = -13 $$
- $$ f(0) = 7 $$
- $$ f(4) = 15 $$
$$ f(-4) = -13 $$, $$ f(0) = 7 $$, $$ f(4) = 15 $$.

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

Upstudy AI Solution

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(a)

(b)

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