Determine the end behavior of each function. (a)        f(x) = 14 + 2x2 − 13x3 − x4 f(x) → as x → −∞ f

Important:  express those exponentials using the symbol " ^ ."

Thus:  

f(x) = 14 + 2x^2 − 13x^3 − x^4 

Then, the limit of f(x) → as x → −∞ 

is negative infinity.  the x^4 term dominates all the other terms, and because x^4 is negative, the final limit will be negative (negative infinity).

This is the function written in descending order of power:

And since the highest power is 4 this function behaves like a quadratic (U-shaped).
If the leading coefficient of the function is positive the graph looks like U but if it is negative it looks like ∩.


It is negative so the graph is heading towards -∞ on both sides.
→-∞ as x→-∞

; minimum

Step-by-step explanation:

Given:

The function is,

The given function represent a parabola and can be expressed in vertex form as:

The vertex form of a parabola is , where, is the vertex.

So, the vertex is .

In order to graph the given parabola, we find some points on it.

Let

So, the points are .

Mark these points on the graph and join them using a smooth curve.

The graph is shown below.

From the graph, we conclude that at the vertex , it is minimum.