Polynomial Functions and Models

Shift right 2 and down 5

Shift left 2 and down 5

Shift left 2 and up 5

Shift right 2, reflect on x-axis, and down 5

$$y=3x^3$$

$$y=x^3$$

$$y=x^2$$

$$y=3x^2$$

the left side of the graph goes up and the right side goes down

the right side of the graph goes up and the left side goes down

both ends of the graph go down

both ends of the graph go up

$$x=0,\ 1$$ and $$y\ =\ 0$$

$$\ x=1$$ and $$y=-6$$

$$x=6,\ 1$$ and $$y=6$$

$$x=-1,\ 0$$ and $$y=0$$

$$x=-3,\ 1$$ and $$y=6$$

$$x=-1,\ 3$$ and $$y=6$$

$$x=2,\ -3,\ 1$$ and $$y=-6$$

$$x=2,\ 3,\ -1$$ and $$y=-6$$

Domain: $$\left(-\infty,\ \infty\right)$$

Range: $$\left[-1,\infty\right)$$

Domain: $$\left(-\infty,\ \infty\right)$$

Range: $$\left(-\infty,\ \infty\right)$$

Domain: $$\left[-1,\ \infty\right)$$

Range: $$\left(-\infty,\ \infty\right)$$

Domain: $$\left(\infty,\ 1\right)$$

Range: $$\left[-1,\ -\infty\right)$$

$$f\left(x\right)=\left(x-5\right)^2\left(x-3\right)$$

$$f\left(x\right)=\left(x-5\right)\left(x-3\right)$$

$$f\left(x\right)=\left(x-5\right)\left(x-3\right)^3$$

$$f\left(x\right)=\left(x-5\right)^2\left(x-3\right)^2$$

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