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Use the image to answer the question.

A coordinate plane with three lines, 2 with 1 open endpoint and 1 with a closed endpoint. The y-axis ranges from negative 5 to 10 in unit increments. The x-axis ranges from -5 to 8 in unit increments.

True or false: The graph represents the piecewise function f(x)=⎧⎩⎨⎪⎪x+2 if x<−25+x if −2≤x<4−2x+7 if x≥4
. Enter 1 for true or 2 for false.

(1 point)

1 answer

To determine if the given graph represents the piecewise function

\[ f(x) = \begin{cases} x + 2 & \text{if } x < -2 \ 5x & \text{if } -2 \leq x < 4 \ -2x + 7 & \text{if } x \geq 4 \end{cases} \]

we need to analyze the endpoints and behavior of each line segment described.

  1. For \( f(x) = x + 2 \) when \( x < -2 \): This is a line with a slope of 1 that intersects the y-axis at (0, 2) and will be open at the endpoint at \( x = -2 \).

  2. For \( f(x) = 5x \) when \( -2 \leq x < 4 \): This is a line with a slope of 5 and includes the point where \( x = -2 \) (closed endpoint) and will be open at \( x = 4 \).

  3. For \( f(x) = -2x + 7 \) when \( x \geq 4 \): This is a line with a negative slope (-2) which will be open at the starting point when \( x = 4 \).

Next, confirm if the graph matches this behavior regarding the open and closed endpoints along the specified intervals.

Since I can’t see the image, I can't conclude definitively, but based on the structure of the piecewise function, if the description matches, the answer would be:

1 for true, otherwise 2 for false.

If you would like a definite answer, please provide descriptive details of the graph or its segments.