Respuesta :

Answer:

It falls to the left and rises to the right.

Step-by-step explanation:

The polynomial function is given as;

g(x) =10x^(9) - 50x^(6) - 500x²

In this polynomial, the leading coefficient is 10. This is positive and also an even number and thus it means the graph will rise to the right.

Also, the degree of the polynomial is 9 since that's the highest degree of x. This degree is odd and it means the graph will point in the opposite direction to that of the leading coefficient. Thus, we can say it falls to the left.

So in summary, the end behavior of the graph of g is that it falls to the left and rises to the right.

facundo3141592

The end behavior of the polynomial is:

  • When x ⇒ ∞, g(x) ⇒ ∞
  • When x ⇒ -∞, g(x) ⇒ -∞

What is the end behavior of the graph of g(x)?

The first thing you need to notice is that the degree of the polynomial is odd. This means that the function will have two opposite end behaviors.

Also, the leading coefficient is positive (is 10). So, when x tends to positive infinity, the end behavior of the function will tend to positive infinity.

When x tends to negative infinity, because the exponent is odd, the outcome will also be negative. Then here the end behavior of the function will tend to negative infinity.

Concluding, we can write:

  • When x ⇒ ∞, g(x) ⇒ ∞
  • When x ⇒ -∞, g(x) ⇒ -∞

If you want to learn more about end behavior, you can read:

https://brainly.com/question/1365136

#SPJ2

Otras preguntas