Mid-Chapter Quiz
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What happens with the values of f(x) as x increases? What about when x decreases?
Is the end behavior the same in both directions?
At how many points does the graph intersect the x-axis?
f(x) → +∞ as x → - ∞
f(x) → - ∞ as x → + ∞
Function: Odd-degree
Real Zeros: 3
End behavior is the behavior of the graph of f(x) as x approaches positive or negative infinity. Let's consider the given graph.
We can see above that as x approaches negative infinity, f(x) approaches positive infinity. As x approaches positive infinity, f(x) approaches negative infinity. f(x) → +∞ as x → - ∞ and f(x) → - ∞ as x → + ∞
From Part A, we know that the end behavior goes in opposite directions on either end. Therefore, the given graph represents an odd-degree function.
| End Behavior | Type of Function |
|---|---|
| Same Direction | Even-degree function |
| Opposite Directions | Odd-degree function |
