A clothing store uses the step function $$ f(x) $$ to recommend jeans sizes as a function of $$ x $$, a child's height in inches. $$ f(x)=\left\{\begin{array}{l}1,40 \leq x

Question

A clothing store uses the step function $$ f(x) $$ to recommend jeans sizes as a function of $$ x $$, a child's height in inches. $$ f(x)=\left\{\begin{array}{l}1,40 \leq x<42 \ 2,42 \leq x<44 \ 3,44 \leq x<46 \ 4,46 \leq x<48\end{array}ight\} $$ According to the function, which is the height of a child who should wear size 2 jeans? 41.9 inches 42 inches 44 inches 44.1 inches

UpStudy AI · Accepted Answer

To determine which height corresponds to size 2 jeans according to the given step function $$ f(x) $$, let's analyze the function:

$$
f(x)=\left\{\begin{array}{ll}
1 & \text{if } 40 \leq x < 42 \
2 & \text{if } 42 \leq x < 44 \
3 & \text{if } 44 \leq x < 46 \
4 & \text{if } 46 \leq x < 48 \
\end{array}\right.
$$

**Size 2 jeans** correspond to the height range where $$ 42 \leq x < 44 $$.

Now, let's evaluate each option:

1. **41.9 inches**
   - $$ 41.9 $$ is **less than 42**, so it falls in the range for size 1 jeans.
   
2. **42 inches**
   - $$ 42 $$ is **exactly 42**, which satisfies $$ 42 \leq x < 44 $$. Thus, this height corresponds to size 2 jeans.

3. **44 inches**
   - $$ 44 $$ is **not less than 44**. It falls at the boundary but does **not** satisfy $$ 42 \leq x < 44 $$. Instead, it starts the range for size 3 jeans.
   
4. **44.1 inches**
   - $$ 44.1 $$ is **greater than 44**, placing it in the range for size 3 jeans.

**Conclusion:** The height that falls within the range for size 2 jeans is **42 inches**.

**Answer:** 42 inches
42 inches

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