Question

which piecewise function best describes the scenario below?

a toll road charges $7 for cars traveling up to 25 miles and $0.30 per mile for each additional mile over 25miles.

\\( f(x) = \

$$\begin{cases} 7 & x \\le 25 \\\\ 0.30(x - 7) & x > 25 \\end{cases}$$

\\)

\\( f(x) = \

$$\begin{cases} 7 & x < 25 \\\\ 7(x - 25) & x > 25 \\end{cases}$$

\\)

\\( f(x) = \

$$\begin{cases} 7 & x \\le 25 \\\\ 7 + 0.30(x - 25) & x > 25 \\end{cases}$$

\\)

\\( f(x) = \

$$\begin{cases} 7 & x > 25 \\\\ 7 + 0.30(x - 25) & x < 25 \\end{cases}$$

\\)

Explanation:

Analyze the first interval

Using the Piecewise Functions knowledge point

$$ \text{For } x \le 25, \quad F(x) = 7 $$

Analyze the second interval

Using the Piecewise Functions knowledge point

$$ \text{For } x > 25, \quad F(x) = 7 + 0.30(x - 25) $$

Combine into a piecewise function

Using the Piecewise Functions knowledge point

$$ F(x) =
LATEXBLOCK0
$$

Answer:

• (A) \(F(x) =

$$\begin{cases} 7 & x \le 25 \\ 0.30(x - 7) & x > 25 \end{cases}$$

\)

• (B) \(F(x) =

$$\begin{cases} 7 & x < 25 \\ 7(x - 25) & x > 25 \end{cases}$$

\)

• **(C) \(F(x) =

$$\begin{cases} 7 & x \le 25 \\ 7 + 0.30(x - 25) & x > 25 \end{cases}$$

\) (Correct answer)**

• (D) \(F(x) =

$$\begin{cases} 7 & x > 25 \\ 7 + 0.30(x - 25) & x < 25 \end{cases}$$

\)