Given the function f(x) = −3x^3 + 9x^2 − 2x + 3, what part of the function indicates that the left end starts at the top of the graph? A) The degree of the first term B) The coefficient of the first term
Mathematics · High School · Thu Feb 04 2021
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The part of the function that indicates that the left end starts at the top of the graph is.
B) The coefficient of the first term.
In the function f(x) = −3x^3 + 9x^2 − 2x + 3, the first term is −3x^3. The coefficient of this term is −3, and the degree of the first term is 3, which is an odd number. Two key features determine the end behavior of the graph for a polynomial function like this one: the leading coefficient (in this case, −3) and the degree of the function (which here is 3).
For polynomial functions with odd degrees, the ends of the graph will go off in opposite directions. If the leading coefficient is positive, the right end of the graph will go towards positive infinity, and the left end will go towards negative infinity. Conversely, if the leading coefficient is negative, as it is in this case, the right end of the graph will go towards negative infinity, and the left end will go towards positive infinity. That's why the leading coefficient being negative is what indicates that the left end starts at the top of the graph