The function passes through the origin.

The function has a zero at -3.

The function has a local maximum at (-1.76, -3.46).

The function has an x-intercept at (3,0).

y = –0.5x³ + 0.25x² – 1.25x – 2

y = 0.25x³ + 0.75x² – 1.5x – 2

y = 1.5x⁴ + 0.25x² – 0.5x – 2

y = –0.75x⁴ + 1.25x³ – 0.5x² – 2x

$$\left(-\infty,-1\right)$$  

$$\left(-1,2\right)$$  

$$\left(2,\infty\right)$$  

$$\left(-\infty,\infty\right)$$  

x = 3 and x = -7

x = 3

x = -7

x = -4

(2/3, 0)

(4,0) (-2,0)

(-8,0) (1,0)

(-4,0) (2,0)

$$x=-3$$  

$$x=-2$$  

$$x=0$$  

$$x=1$$  

$$x=3$$  

D : All real numbers, x ≠ -2
R: All real number y≠ 1

D : All real numbers, x ≠ 2

R: All real number y≠ 1

D : All real number x ≠ -2
R: All real number y≠ -1

D : All real number x ≠ 1
R: All real number y≠ 2

D : All real numbers, x ≠ -1
R: All real number y≠ 2

As x → -∞, y → -∞.

As x → ∞, y → ∞.

As x → -∞, y → ∞.

As x → ∞, y → -∞.

As x → -∞, y → 1.

As x → ∞, y → 1.

As x → -∞, y → 2.

As x → ∞, y → 2.

r = 4

r = 8

r = 4sin(Θ)

r = 8sin(Θ)

r = 4sin(Θ)

r = -2sin(Θ)

r = 2cos(Θ)

r = -4cos(Θ)

A limacon with an inner loop

A dimpled limacon

A cardiod

A rose