Answer:
- Right: x → ∞, f(x) → ∞
- Left: x → -∞, f(x) → -∞
- degree: 3
Explanation:
You want the end behavior and degree of the function shown in the graph.
End behavior
As you have noted, the leading coefficient is positive, and the function is of odd degree.
When the function is of odd degree, the sign of the leading coefficient multiplies the x-value to define the end behavior. Since the leading coefficient is positive, the end behavior sign matches the x behavior sign.
To the right, x → +∞. The sign of f(x) matches that: f(x) → +∞.
To the left, x → -∞. The sign of f(x) matches that: f(x) → -∞.
Degree
The degree of the function is at least 1 more than the number of turning points (relative extrema). There are 2 turning points, so the degree is 3.
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