Please describe the end behavior of the graph of the function below.
f(x) = –2x^5 – x^3 + x – 5?
The end behavior for positive x will be large negative. The end behavior for negative x will be large positive.
Does this mean that it will be Upward to the left and downward to the right?
To determine the end behavior of the graph of the function f(x) = -2x^5 - x^3 + x - 5, we need to examine the leading term of the polynomial, which is -2x^5.
The leading term of a polynomial determines the behavior of the polynomial as x approaches positive infinity and negative infinity.
In this case, the leading coefficient is negative (-2), which indicates that the graph of the function will approach negative infinity as x approaches positive infinity. This means that the graph will decrease without bound as x becomes larger and larger.
Similarly, as x approaches negative infinity, the graph will also decrease without bound.
Therefore, the end behavior of the graph of the function f(x) = -2x^5 - x^3 + x - 5 is that it will decrease without bound as x approaches both positive infinity and negative infinity.
To determine the end behavior of the graph of the function, you need to examine the leading term of the polynomial function.
In this case, the leading term is -2x^5.
The degree of the leading term is odd (5), and the coefficient of the leading term is negative (-2). These two pieces of information can help us determine the end behavior.
When the degree of the leading term is odd and the coefficient is positive, the function will increase without bound as x approaches negative infinity and decrease without bound as x approaches positive infinity.
However, when the coefficient of the leading term is negative, the behavior is reversed.
Therefore, the end behavior of the graph of the function f(x) = –2x^5 – x^3 + x – 5 is as follows:
As x approaches negative infinity, the graph will decrease without bound (downward).
And as x approaches positive infinity, the graph will increase without bound (upward).