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.

Question

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)

Answer 1

To determine if the given piecewise function \( f(x) \) matches the graph described, we need to analyze the segments of the function and the conditions given.

The piecewise function is:

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

1. First case: \( x + 2 \) if \( x < -2 \) – This is a line with a slope of 1, starting from a point when \( x = -2 \) (which is open).

2. Second case: \( 5 + x \) if \( -2 \leq x < 4 \) – This line starts from \( ( -2, -2 + 5 ) = (-2, 3) \) and goes to \( (4, 4 + 5) = (4, 9) \). The endpoint at -2 is closed and at 4 is open.

3. Third case: \( -2x + 7 \) if \( x \geq 4 \) – This line starts from the point at \( x = 4 \) (which is closed) and continues downwards.

From your description, it seems that the lines have endpoints that are consistent with the conditions laid out in the piecewise function.

Conclusion: It appears that the graph of the piecewise function described matches your description. Hence, the statement is True.

Answer: 1