Question
Choose the correct end behavior for the function graphed.
The main points are(-5.175,0) (-1,-5) (1.175,0)
(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 ∞
The main points are(-5.175,0) (-1,-5) (1.175,0)
(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 correct end behavior of the function based on the points you provided (-5.175, 0), (-1, -5), and (1.175, 0), we should analyze how the function behaves as \( x \) approaches \( -\infty \) and \( \infty \).
From the provided points, we can see:
- The function crosses the x-axis at the points (-5.175, 0) and (1.175, 0), indicating that these are x-intercepts.
- The point (-1, -5) suggests that the function has a local minimum around this region.
Given that the function has x-intercepts at the two negative and positive x-values, we can infer the following general behavior:
- As \( x \) approaches \( -\infty \), if the function starts above the x-axis (which is typical for polynomials that cross the x-axis), it will likely descend to \( -\infty \).
- As \( x \) approaches \( \infty \), since it has a crossing at (1.175, 0), it likely rises after that point, possibly going towards \( +\infty \).
Thus, the end behavior of the function should be:
- As \( x \) approaches \( -\infty \), \( f(x) \) approaches \( -\infty \).
- As \( x \) approaches \( \infty \), \( f(x) \) approaches \( \infty \).
Based on this analysis, the correct response is:
**as x approaches −∞, f(x) approaches −∞ and as x approaches ∞, f(x) approaches ∞.**
From the provided points, we can see:
- The function crosses the x-axis at the points (-5.175, 0) and (1.175, 0), indicating that these are x-intercepts.
- The point (-1, -5) suggests that the function has a local minimum around this region.
Given that the function has x-intercepts at the two negative and positive x-values, we can infer the following general behavior:
- As \( x \) approaches \( -\infty \), if the function starts above the x-axis (which is typical for polynomials that cross the x-axis), it will likely descend to \( -\infty \).
- As \( x \) approaches \( \infty \), since it has a crossing at (1.175, 0), it likely rises after that point, possibly going towards \( +\infty \).
Thus, the end behavior of the function should be:
- As \( x \) approaches \( -\infty \), \( f(x) \) approaches \( -\infty \).
- As \( x \) approaches \( \infty \), \( f(x) \) approaches \( \infty \).
Based on this analysis, the correct response is:
**as x approaches −∞, f(x) approaches −∞ and as x approaches ∞, f(x) approaches ∞.**