Question

Which function matches the graph?



(1 point)
Responses


g(x)={−x + 1, x ≤−43, x > −4
g(x)={−x + 1, x ≤−43, x > −4


g(x)={−x, x < −43, x ≥−4
g(x)={−x, x < −43, x ≥−4

Answer 1

To determine which function matches a specific graph, we need a description of the graph in question, such as key points, behavior, and any transitions at particular values of \(x\). However, I can provide some analysis based on the two piecewise functions given:

1. **Function 1**:
\[
g(x) =
\begin{cases}
-x + 1 & \text{if } x \leq -4 \\
3 & \text{if } x > -4
\end{cases}
\]
- For \(x \leq -4\), the function is a line with a slope of -1 and y-intercept at 1. When \(x = -4\), \(g(-4) = -(-4) + 1 = 5\).
- For \(x > -4\), the function is constant at \(y = 3\).

2. **Function 2**:
\[
g(x) =
\begin{cases}
-x & \text{if } x < -4 \\
3 & \text{if } x \geq -4
\end{cases}
\]
- For \(x < -4\), again, the function is a line with a slope of -1 (the y-intercept is 0).
- For \(x \geq -4\), the function is constant at \(y = 3\), transitioning from the line to a constant value at \(x = -4\).

### Summary:
- **Both functions will be linear with a slope of -1 for values less than or equal to -4 but will change to the constant \(3\) for \(x > -4\)**.

To decide which graph matches, look for these features:
- A steep decline (the line) for \(x < -4\) and a flat line at \(y = 3\) for \(x \geq -4\).

If the graph has these transitions, the corresponding function would be confirmed. Please compare the description provided here with the actual graph you are looking at to select the correct function.