Question

clothing store uses the step function f(x) to recommend jeans sizes as a function of x, a childs height in inches.\\(f(x) = \

$$\begin{cases} 1, & 40 \\leq x < 42 \\\\ 2, & 42 \\leq x < 44 \\\\ 3, & 44 \\leq x < 46 \\\\ 4, & 46 \\leq x < 48 \\end{cases}$$

\\)according to the function, which is the height of a child who should wear size 2 jeans?\\(\bigcirc\\) 41.9 inches\\(\bigcirc\\) 42 inches\\(\bigcirc\\) 44 inches\\(\bigcirc\\) 44.1 inches

Explanation:

Step1: Identify the interval for size 2

From the step function, size 2 corresponds to \(42 \leq x < 44\).

Step2: Check each option

• 41.9 inches: \(41.9 < 42\), so not in \(42 \leq x < 44\).
• 42 inches: \(42 \leq 42 < 44\), satisfies the interval.
• 44 inches: \(44\) is not less than \(44\) (the upper bound is exclusive), so not in \(42 \leq x < 44\).
• 44.1 inches: \(44.1 > 44\), so not in \(42 \leq x < 44\).

Answer:

B. 42 inches