Question
graph shows a line in the (+,-) part of the graph curving and passing through (0,-2) and (0.6,0)
What is the end behavior of the function shown in the graph above?
(1 point)
Responses
As x approaches −∞, f(x) approaches ∞.
As x approaches ∞, f(x) approaches −3.
As x approaches −∞, f(x) approaches ∞.
As x approaches ∞, f(x) approaches −3.
As x approaches 0, f(x) approaches ∞.
As x approaches ∞, f(x) approaches −∞.
As x approaches 0, f(x) approaches ∞.
As x approaches ∞, f(x) approaches −∞.
As x approaches −∞, f(x) approaches 0.
As x approaches ∞, f(x) approaches ∞.
As x approaches −∞, f(x) approaches 0.
As x approaches ∞, f(x) approaches ∞.
As x approaches 0, f(x) approaches −3.
As x approaches −3, f(x) approaches 0.
What is the end behavior of the function shown in the graph above?
(1 point)
Responses
As x approaches −∞, f(x) approaches ∞.
As x approaches ∞, f(x) approaches −3.
As x approaches −∞, f(x) approaches ∞.
As x approaches ∞, f(x) approaches −3.
As x approaches 0, f(x) approaches ∞.
As x approaches ∞, f(x) approaches −∞.
As x approaches 0, f(x) approaches ∞.
As x approaches ∞, f(x) approaches −∞.
As x approaches −∞, f(x) approaches 0.
As x approaches ∞, f(x) approaches ∞.
As x approaches −∞, f(x) approaches 0.
As x approaches ∞, f(x) approaches ∞.
As x approaches 0, f(x) approaches −3.
As x approaches −3, f(x) approaches 0.
Answers
GPT-4o mini
To determine the end behavior of the function based on the information provided, we note the key points:
1. The line is in the (-,+) part of the graph, which means that at least one portion of the function is in the negative x-axis and positive y-axis regions.
2. The function passes through the points (0,-2) and (0.6, 0).
From this information, we can deduce the following about the end behavior:
- The function passes through (0, -2) indicating that when \( x = 0 \), \( f(x) = -2 \).
- The function reaches (0.6, 0), thus moving from a negative value to the x-axis indicates that as \( x \) increases, \( f(x) \) increases towards 0 and eventually becomes positive.
Now, considering limits:
- As \( x \) approaches \( -\infty \): Since the line is curving in the (-,+) area and there are no vertical asymptotes mentioned, we would likely expect \( f(x) \) to approach \( \infty \).
- As \( x \) approaches \( \infty \): As the function continues to increase from negative to zero and possibly beyond, it likely approaches \( \infty \) or at least does not go to negative values.
Given these points, the most plausible responses from your choices about end behavior would be:
- **As \( x \) approaches \(-\infty\), \( f(x) \) approaches \(\infty\)**.
- **As \( x \) approaches \(\infty\), \( f(x) \) approaches \(\infty\)**.
However, since we're given responses, please select:
- **As \( x \) approaches \( -\infty\), \( f(x) \) approaches \(\infty\). As \( x \) approaches \(\infty\), \( f(x) \) approaches \(\infty\)**.
Note that not all options reflect this exactly; you may have to choose the closest or a single one depending on your given selections.
1. The line is in the (-,+) part of the graph, which means that at least one portion of the function is in the negative x-axis and positive y-axis regions.
2. The function passes through the points (0,-2) and (0.6, 0).
From this information, we can deduce the following about the end behavior:
- The function passes through (0, -2) indicating that when \( x = 0 \), \( f(x) = -2 \).
- The function reaches (0.6, 0), thus moving from a negative value to the x-axis indicates that as \( x \) increases, \( f(x) \) increases towards 0 and eventually becomes positive.
Now, considering limits:
- As \( x \) approaches \( -\infty \): Since the line is curving in the (-,+) area and there are no vertical asymptotes mentioned, we would likely expect \( f(x) \) to approach \( \infty \).
- As \( x \) approaches \( \infty \): As the function continues to increase from negative to zero and possibly beyond, it likely approaches \( \infty \) or at least does not go to negative values.
Given these points, the most plausible responses from your choices about end behavior would be:
- **As \( x \) approaches \(-\infty\), \( f(x) \) approaches \(\infty\)**.
- **As \( x \) approaches \(\infty\), \( f(x) \) approaches \(\infty\)**.
However, since we're given responses, please select:
- **As \( x \) approaches \( -\infty\), \( f(x) \) approaches \(\infty\). As \( x \) approaches \(\infty\), \( f(x) \) approaches \(\infty\)**.
Note that not all options reflect this exactly; you may have to choose the closest or a single one depending on your given selections.