Unit 5: Key features and Characteristics of polynomials

  $$As\ \ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow-\infty$$   $$As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$$  

$$As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$$   $$As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$$  

$$As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$$  

$$As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$$  

$$As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$$  

$$As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$$  

odd degree

even degree

positive leading coefficient

negative leading coefficient

y = (x -3)(x + 1)(x +2)

y = −(x + 3)(x + 1)(x − 2)

y = −(x − 3)(x + 1)(x + 2)

y = (x + 3)(x + 1)(x + 2)

-1

1

-2

-3

(-3, 1)

(-∞, -5) ∪ (0, 2)

(-∞, -3) ∪ (1, ∞)

(-5, 0) ∪ (2, ∞)

The domain is (-∞,+∞)

The range is (-∞,+∞)

the linear factors are $$\left(x-3\right)\left(x+2\right)^2\left(x+5\right)$$

multiplicity of 2 at x=2

There are 2 local minimum, and 1 local maximum