Polynomial Functions: Domain, Range, X-Intercepts, Multiplicity

The domain is all real numbers.

The range is $$\left(-\infty,\ +\infty\right)$$  .

The domain is $$\left(-\infty,+\infty\right)$$  

The range is $$y\ge-4$$  

{ -5,-3 }

{-2, -5}

{0,-5}

{0,-2}

x = - 4

There are none

x = - 1.5 & 1.5

x = - 3.5 and 3.5

(-∞, ∞)

[7, ∞)

(-∞, 7]

(-1, 1)

(-∞, 7)

(-∞, ∞)

(7, ∞)

(-∞, 7)

(-1, 1)

1

2

3

4

2

1

4

3

2 crosses, 1 crosses, -3 bounce, -4 bounce   

1 crosses, -3 bounce, - 4 crosses

1 crosses, -3 bounce, -4 bounce 

1 bounce, -3 crosses, -4 crosses  

$$f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x-7\right)$$

$$f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x+7\right)$$

$$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^2\left(x-7\right)^2$$

$$f\left(x\right)=\left(x-1\right)^2\left(x+2\right)^2\left(x+7\right)^2$$