Two lines, a solid line and a dotted line, are drawn on a coordinate plane. Both the x-axis and y-axis range from negative 4 to 4 in 1-unit increments.

Question

Create a piecewise function that represents the graph.

(1 point)
Responses

f(x)={1,2x−1,−3<x≤−1−1<x<1
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 x less-than-or-equal-to negative 1 2nd Row 1st Column 2 x minus 1 comma 2nd Column negative 1 less than x less than 1 End Matrix

f(x)={x+1,2x−1, −3≤x<−1−1≤x≤1
f left parenthesis x right parenthesis equals left brace Start 2 by 2 Matrix 1st Row 1st Column x plus 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

f(x)={1,2x, −3≤x<−1−1≤x≤1
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 comma 2nd Column negative 1 less-than-or-equal-to x less-than-or-equal-to 1 End Matrix

f(x)={1,2x−1,−3≤x<−1−1≤x≤1

Answer 1

To determine the correct piecewise function, we need to analyze the given conditions of the lines on the coordinate plane.

We have two segments defined by their behaviors in different intervals:

1. For the interval \(-3 \leq x < -1\): The line is constant, which indicates that the function value is a fixed number. Given the choices, this could be \(f(x) = 1\).

2. For the interval \(-1 \leq x \leq 1\): The line appears to follow a linear equation. The options suggest that this could be \(f(x) = 2x - 1\).

Now, we compile these insights into a piecewise function:

The correct option which represents the graph based on the analysis is: \[ f(x) = \begin{cases} 1 & \text{for } -3 \leq x < -1 \ 2x - 1 & \text{for } -1 \leq x \leq 1 \end{cases} \]

So, the correct response from the provided choices is: f(x)={1,2x−1,−3≤x<−1−1≤x≤1.