consider the function g(x)=x^5 - 3x^4. part: 0 / 4 part 1 of 4 the end - behavior of the function is (choose…

consider the function g(x)=x^5 - 3x^4. part: 0 / 4 part 1 of 4 the end - behavior of the function is (choose one) to the left and (choose one) to the right.

consider the function g(x)=x^5 - 3x^4. part: 0 / 4 part 1 of 4 the end - behavior of the function is (choose one) to the left and (choose one) to the right.

Answer

Explanation:

Step1: Identify the leading - term

The leading - term of the polynomial function (g(x)=x^{5}-3x^{4}) is (x^{5}) since the term with the highest power of (x) is (x^{5}).

Step2: Analyze the end - behavior based on the degree and leading coefficient

The degree (n = 5) (an odd number) and the leading coefficient (a = 1) (positive). For a polynomial function (y = a x^{n}) with (n) odd and (a>0), as (x\to-\infty), (y\to-\infty) and as (x\to+\infty), (y\to+\infty).

Answer:

Decreases to the left and increases to the right.