Question
rue 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.
$$
. Enter 1 for true or 2 for false.
$$
Answers
GPT-4o mini
To determine whether the statement is true or false, we need to analyze the piecewise function given:
\[
f(x) =
\begin{cases}
x + 2 & \text{if } x < -2 \\
x & \text{if } -2 \leq x < 4 \\
-2x + 7 & \text{if } x \geq 4
\end{cases}
\]
Now, let's break down each piece of the function:
1. **For \( x < -2 \)**: The function is defined as \( f(x) = x + 2 \).
2. **For \( -2 \leq x < 4 \)**: The function is defined as \( f(x) = x \).
3. **For \( x \geq 4 \)**: The function is defined as \( f(x) = -2x + 7 \).
Because the description in the question appears to have some errors (e.g., 25 should be -2 in the first case and possibly wrong values in the ranges), we can determine if the graph matches the provided piecewise function based on these segments.
To confirm whether the graph represents this specific piecewise function, we'd need to actually see the graph in question. However, if we assume there was a typo and that it was meant to represent the function as described above accurately, we can proceed accordingly.
If the graph matches the domains and the corresponding function values as defined by the piecewise function, we would mark it as true (1). However, if it does not, then it would be marked false (2).
If you can verify or provide the graph for more precise analysis, that would help clarify the assertion. For now, based on typical notation and assuming it properly represents the defined function, I would suggest:
1 = true (if it accurately represents the function)
2 = false (if it does not accurately reflect the function)
Without the graph present, I cannot definitively answer true or false, so please check your graph against the piecewise function provided above.
\[
f(x) =
\begin{cases}
x + 2 & \text{if } x < -2 \\
x & \text{if } -2 \leq x < 4 \\
-2x + 7 & \text{if } x \geq 4
\end{cases}
\]
Now, let's break down each piece of the function:
1. **For \( x < -2 \)**: The function is defined as \( f(x) = x + 2 \).
2. **For \( -2 \leq x < 4 \)**: The function is defined as \( f(x) = x \).
3. **For \( x \geq 4 \)**: The function is defined as \( f(x) = -2x + 7 \).
Because the description in the question appears to have some errors (e.g., 25 should be -2 in the first case and possibly wrong values in the ranges), we can determine if the graph matches the provided piecewise function based on these segments.
To confirm whether the graph represents this specific piecewise function, we'd need to actually see the graph in question. However, if we assume there was a typo and that it was meant to represent the function as described above accurately, we can proceed accordingly.
If the graph matches the domains and the corresponding function values as defined by the piecewise function, we would mark it as true (1). However, if it does not, then it would be marked false (2).
If you can verify or provide the graph for more precise analysis, that would help clarify the assertion. For now, based on typical notation and assuming it properly represents the defined function, I would suggest:
1 = true (if it accurately represents the function)
2 = false (if it does not accurately reflect the function)
Without the graph present, I cannot definitively answer true or false, so please check your graph against the piecewise function provided above.