Understanding the End Behavior of a Polynomial Function

What is the end behavior of the graph of the polynomial function f(x) = 3x^6 + 30x^5 + 75x^4?

The end behavior of a polynomial function is determined by the degree and leading coefficient of the polynomial. In this case, the given polynomial function is f(x) = 3x^6 + 30x^5 + 75x^4.

The degree of the polynomial function is 6, and the leading coefficient is 3. When a polynomial function has an even degree and a positive leading coefficient, like in this case, the end behavior of the graph will be as follows:

• As x approaches negative infinity, f(x) -> infinity
• As x approaches positive infinity, f(x) -> infinity

Therefore, the end behavior of the graph of the polynomial function f(x) = 3x^6 + 30x^5 + 75x^4 is that the graph will rise on both ends as x approaches negative and positive infinity.

What is the ratio 6:18?

The ratio 6:18 simplifies to 1:3.

What is the ratio 48:16?

The ratio 48:16 simplifies to 3:1.