Math

QuestionFind the end behavior of the polynomial function f(x)=4x5+5x44x3f(x) = 4x^5 + 5x^4 - 4x - 3.

Studdy Solution

STEP 1

Assumptions1. The function given is a polynomial function. . The function is f(x)=4x5+5x44x3f(x) =4x^5 +5x^4 -4x -3.
3. We are interested in the end behavior of this function, which refers to the behavior of the function as xx approaches positive or negative infinity.

STEP 2

The end behavior of a polynomial function is determined by the term with the highest degree, also known as the leading term. In this case, the leading term is 4x54x^5.

STEP 3

The degree of the leading term is5, which is an odd number. This means that the end behavior of the function will differ as xx approaches positive infinity and as xx approaches negative infinity.

STEP 4

The coefficient of the leading term is4, which is a positive number. This means that as xx approaches positive infinity, f(x)f(x) will also approach positive infinity.

STEP 5

Because the degree of the leading term is odd and the coefficient is positive, as xx approaches negative infinity, f(x)f(x) will approach negative infinity.
So, the end behavior of the function f(x)=4x5+5x44x3f(x) =4x^5 +5x^4 -4x -3 is as followsAs xx approaches positive infinity, f(x)f(x) approaches positive infinity. As xx approaches negative infinity, f(x)f(x) approaches negative infinity.

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