To construct the piecewise function representing the graph with the given constraints, we will analyze the function in regions defined by the x-values.
Assuming that the solid line corresponds to the function \( f(x) = 2x - 1 \) and is only valid for \( -1 < x < 1\), and that a constant function \( f(x) = 1 \) is valid for \( -3 \leq x < -1\), we can represent this using a piecewise function as follows:
Given the information provided together with common piecewise structures:
- It seems that for \( -3 \leq x < -1 \), the function equals 1.
- For \( -1 \leq x < 1 \), the function equals \( 2x - 1 \).
Thus, the piecewise function can be represented as:
\[ f(x) = \begin{cases} 1 & \text{if } -3 \leq x < -1 \ 2x - 1 & \text{if } -1 \leq x < 1 \end{cases} \]
Now, let's match this with the provided options. The correct form looks like:
f(x) = {1, 2x - 1, -3 ≤ x < -1; -1 ≤ x < 1}
Based on the responses you provided, the last one, which follows the structure I defined, seems to denote:
f left parenthesis x right parenthesis equals left brace Start 2 by 2 Matrix 1st Row 1st Column 1 comma 2nd Column negative 3 less-than-or-equal-to x less than negative 1 2nd Row 1st Column 2 x minus 1 comma 2nd Column negative 1 less-than-or-equal-to x less-than-or-equal-to 1 End Matrix.
Thus, the correct answer is: f(x)={1,2x−1,−3≤x<−1,−1≤x<1.