Question

Describe the end behavior of F(x) = x^2 + 4x +3

Answer 1

The end behavior of the function F(x) = x^2 + 4x + 3 is an upward opening graph on both ends.

Step-by-step explanation:

The end behavior of a polynomial function can be determined by examining the leading term. In the given function, F(x) = x^2 + 4x + 3, the leading term is x^2. Since the degree of the leading term is 2, we can conclude that the end behavior of the function is the same as that of a quadratic function. As x approaches positive or negative infinity, the value of x^2 increases without bound, resulting in a graph that opens upwards on both ends.

Answer 2

see the explanation

Step-by-step explanation:

we know that

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph

In this problem

we have

`f)x)=x^2+4x+3`

Is a vertical parabola open upward (the vertex is a minimum)

The degree of the function is even (2) and the leading coefficient is positive.

So,

the end behavior is:

f(x)→+∞, as x→−∞

f(x)→+∞, as x→+∞