Given function:
In order to graph it, let us find some coordinates for the given function to plot on graph.
Let us find the x-intercepts first by setting given function equal to 0.
x^3 + 6x^2 + 8x =0.
Factoring out x.
x(x^2+6x+8) = 0
Factoring quadratic x^2 +6x +8, we get
x(x+2)(x+4) =0
Applying zeros product rule, we get
x =0
x+2 = 0 => x = -2
x+4 =0 => x = -4.
Therefore, we got x-intercepts (0,0), (-2,0) and (-4,0).
Because degree is 3 and leading coefficient a positive number, the graph would go down on the left and go up on the right.
From the graph we can see end behaviour:
x⇒∞, y⇒∞
x⇒-∞, y⇒-∞