5)
For function f(x) = x³ - 3x² + 6, here the highest degree of the polynomial is 3 which is an odd number.
For a polynomial, if the highest degree is odd, it means the ends of the graph will go in opposite directions. In this function, the leading coefficient is 1, which is positive.
Accordingly, we denote its end behavior as "down, up":
- x → ∞ ⇒ f(x) → ∞
- x → - ∞ ⇒ f(x) → - ∞
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7)
For function f(x) = 2x² + 12x + 17, the highest degree of the function is 2, which is an even number.
That means the ends of this graph will go in the same direction.
Additionally, the leading coefficient in this function is 2, which is positive. Hence, the ends of the function graph both go upwards.
The end behavior of this function can thus be represented as "up, up".
- x → ∞ ⇒ f(x) → ∞
- x → - ∞ ⇒ f(x) → ∞