Question
Choose the correct end behavior for the function graphed.
graph shows a line passing through (-3.1,0) and (1.1,0) and the line curves at (-1,-5)
(1 point)
Responses
as x approaches −∞, f(x) approaches −∞
and as x approaches ∞, f(x) approaches ∞
as x approaches −∞, f(x) approaches −∞
and as x approaches ∞, f(x) approaches ∞
as x approaches −∞, f(x) approaches ∞
and as x approaches ∞, f(x) approaches ∞
as x approaches −∞, f(x) approaches ∞
and as x approaches ∞, f(x) approaches ∞
as x approaches −∞, f(x) approaches −∞
and as x approaches ∞, f(x) approaches −∞
as x approaches −∞, f(x) approaches −∞
and as x approaches ∞, f(x) approaches −∞
as x approaches −∞, f(x) approaches ∞
and as x approaches ∞, f(x) approaches −∞
graph shows a line passing through (-3.1,0) and (1.1,0) and the line curves at (-1,-5)
(1 point)
Responses
as x approaches −∞, f(x) approaches −∞
and as x approaches ∞, f(x) approaches ∞
as x approaches −∞, f(x) approaches −∞
and as x approaches ∞, f(x) approaches ∞
as x approaches −∞, f(x) approaches ∞
and as x approaches ∞, f(x) approaches ∞
as x approaches −∞, f(x) approaches ∞
and as x approaches ∞, f(x) approaches ∞
as x approaches −∞, f(x) approaches −∞
and as x approaches ∞, f(x) approaches −∞
as x approaches −∞, f(x) approaches −∞
and as x approaches ∞, f(x) approaches −∞
as x approaches −∞, f(x) approaches ∞
and as x approaches ∞, f(x) approaches −∞
Answers
Answered by
GPT-4o mini
To determine the end behavior of the function based on the description provided, let's analyze the given information:
- The function passes through the x-intercepts (-3.1, 0) and (1.1, 0), indicating that the function crosses the x-axis at these points.
- The function has a curving point at (-1, -5), which suggests that at this point, the function has a local minimum or maximum.
Since the line curves downwards to the point (-1, -5) and then curves back upwards, we can infer the following about the end behavior:
- As \( x \) approaches \( -\infty \) (moving to the left), the function is likely approaching negative infinity, because it appears that the curve begins at a higher position (above the x-axis) and dips down to (-1, -5).
- As \( x \) approaches \( \infty \) (moving to the right), the function is likely increasing and thus approaches positive infinity after passing the x-intercept at (1.1, 0).
Therefore, the correct end behavior is:
**as \( x \) approaches \( -\infty \), \( f(x) \) approaches \( -\infty \) and as \( x \) approaches \( \infty \), \( f(x) \) approaches \( \infty \)**.
This corresponds to the first response option.
- The function passes through the x-intercepts (-3.1, 0) and (1.1, 0), indicating that the function crosses the x-axis at these points.
- The function has a curving point at (-1, -5), which suggests that at this point, the function has a local minimum or maximum.
Since the line curves downwards to the point (-1, -5) and then curves back upwards, we can infer the following about the end behavior:
- As \( x \) approaches \( -\infty \) (moving to the left), the function is likely approaching negative infinity, because it appears that the curve begins at a higher position (above the x-axis) and dips down to (-1, -5).
- As \( x \) approaches \( \infty \) (moving to the right), the function is likely increasing and thus approaches positive infinity after passing the x-intercept at (1.1, 0).
Therefore, the correct end behavior is:
**as \( x \) approaches \( -\infty \), \( f(x) \) approaches \( -\infty \) and as \( x \) approaches \( \infty \), \( f(x) \) approaches \( \infty \)**.
This corresponds to the first response option.