Questions: Which graph represents the following piecewise defined function? f(x)= -2x, x<-1 -1, -1 ≤ x<2 x-1, x ≥ 2

Transcript text: Which graph represents the following piecewise defined function? \[ f(x)=\left\{\begin{array}{l} -2 x, x<-1 \\ -1,-1 \leq x<2 \\ x-1, x \geq 2 \end{array}\right. \]

Solution

Solution Steps

Step 1: Understand the piecewise function

The given piecewise function is: \[ f(x) = \begin{cases} -2x, & x < -1 \\ -1, & -1 \leq x < 2 \\ x^2, & x \geq 2 \end{cases} \]

Step 2: Analyze each piece of the function

For \( x < -1 \), the function is \( f(x) = -2x \).
For \( -1 \leq x < 2 \), the function is \( f(x) = -1 \).
For \( x \geq 2 \), the function is \( f(x) = x^2 \).

Step 3: Match the function pieces to the graphs

For \( x < -1 \), the graph should show a line with a slope of -2.
For \( -1 \leq x < 2 \), the graph should show a horizontal line at \( y = -1 \).
For \( x \geq 2 \), the graph should show a parabola opening upwards starting from \( x = 2 \).

Final Answer

The correct graph is the one that matches all three conditions. From the given options, the graph in the bottom right (option D) correctly represents the piecewise function.

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