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.

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

1 answer

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.

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