To predict the end-behavior of a polynomial function, first check whether the function is odd-degree or even-degree function and whether the leading coefficient is positive or negative. If you add a negative number you move to the. Degreeį ( x ) → + ∞, as x → − ∞ f ( x ) → + ∞, as x → + ∞į ( x ) → − ∞, as x → − ∞ f ( x ) → − ∞, as x → + ∞į ( x ) → − ∞, as x → − ∞ f ( x ) → + ∞, as x → + ∞į ( x ) → + ∞, as x → − ∞ f ( x ) → − ∞, as x → + ∞ Adding or subtracting a negative number goes in the opposite direction to adding or subtracting a positive number. So, the sign of the leading coefficient is sufficient to predict the end behavior of the function. Quadrant II: The second quadrant is in the. Both x and y have positive values in this quadrant. Quadrant I: The first quadrant is in the upper right-hand corner of the plane. And they also want to do it to negative numbers not negative exponents. Each graph quadrant has a distinct combination of positive and negative values. A negative exponent on the denominator means move it to the top, while a negative exponent on the numerator means move it to the bottom.' They understand it for basic Algebra 1 problems, but not for more complex problems. The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers. There are four graph quadrants that make up the Cartesian plane. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph. The end behavior of a polynomial function is the behavior of the graph of f ( x ) as x approaches positive infinity or negative infinity.
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