Question

c(x) = \

$$\begin{cases} 100 & 0 < x \\leq 10 \\\\ 200 & 10 < x \\leq 20 \\\\ 300 & 20 < x \\leq 30 \\end{cases}$$

function c is the cost for x, amount of people to enter the park. what is the cost if x = 8? options: 200, 100, undefined, 300

Explanation:

Step1: Identify the interval for \( x = 8 \)

We check which piece of the piece - wise function \( C(x)\) applies to \( x = 8 \). The intervals are \( 0\lt x\leq10\), \( 10\lt x\leq20\), and \( 20\lt x\leq30\). Since \( 0\lt8\leq10\), we use the first piece of the function.

Step2: Determine the cost from the function

For the interval \( 0\lt x\leq10\), the function \( C(x)=100\). So when \( x = 8\), \( C(8)=100\).

Answer:

100