9)
For function f(x) = - x² - 6x - 7, the highest degree of the function is 2.
For polynomials, if the highest degree is even, it means the ends of the graph will ultimately go in the same direction.
Furthermore, the leading coefficient in this function is -1, which is negative. Therefore, the ends of this polynomial will go downwards.
So the end behavior can be denoted as "down, down":
- x → ∞ ⇒ f(x) → - ∞
- x → - ∞ ⇒ f(x) → - ∞
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11)
For function f(x) = - x³ + 3x² - 3, 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 negative.
Accordingly, we denote its end behavior as "up, down":
- x → ∞ ⇒ f(x) → - ∞
- x → - ∞ ⇒ f(x) → ∞
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13)
For function f(x) = - x³ + 2x² - 3, 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 negative.
Accordingly, we denote its end behavior as "up, down":
- x → ∞ ⇒ f(x) → - ∞
- x → - ∞ ⇒ f(x) → ∞