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Answers to various questions related to ap precalculus concepts, including increasing and decreasing functions, relative and absolute extrema, concavity, points of inflection, zeros, and end behavior. It also covers topics such as function definition, linear and quadratic functions, even and odd functions, domain, range, independent and dependent variables, rate of change, and degree of a polynomial.
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Increasing Interval - correct answers ✅A function is increasing over its interval of its domain if, as the input values increase, the output values always increase. That is for all a and b in the interval, if a < b then f(a) < f(b) Decreasing Interval - correct answers ✅A function is decreasing over its interval of its domain if, as the input values increase, the output values always decrease. That is for all a and b in the interval, if a < b then f(a) > f(b) Relative minimum - correct answers ✅Where a polynomial function switches between decreasing and increasing or at the included endpoint of a polynomial with a restricted domain Relative maximum - correct answers ✅Where a polynomial function switches between increasing and decreasing or at the included endpoint of a polynomial with a restricted domain Absolute extrema - correct answers ✅Of all local maxima, the greatest is called the global, or absolute, maximum. Likewise, the least of all local minima is called the global, or absolute, minimum.
Concave up - correct answers ✅When the average rate of change over equal length input-value intervals is increasing for all small-length intervals, the graph of the function is concave up Concave down - correct answers ✅When the average rate of change over equal length input-value intervals is decreasing for all small-length intervals, the graph of the function is concave down Point of Inflection - correct answers ✅Points of inflection of a polynomial function occur at input values where the rate of change of the function changes from increasing to decreasing or from decreasing to increasing. This occurs where the graph of a polynomial function changes from concave up to concave down or from concave down to concave up. Zeros - correct answers ✅The graph intersects the x- axis when the output value is zero. The corresponding input values are said to be zeros of the function End behavior - correct answers ✅As input values of a nonconstant polynomial function increase without bound, the output values will either increase or decrease without bound. The corresponding mathematical notation is lim p(x) = ∞ or lim p(x) = -∞
Even functions - correct answers ✅An even function is graphically symmetric over the line x = 0 and analytically has the property f(-x) = f(x) Odd functions - correct answers ✅An odd function is graphically symmetric about the point (0,0) and analytically has the property f(-x) = -f(x) Domain - correct answers ✅the set of input values of a function Range - correct answers ✅the set of output values of a function Independent Variable - correct answers ✅the variable representing the input values of a function Dependent Variable - correct answers ✅the variable representing the output values of a function Rate of Change - correct answers ✅the ratio of the change in the output values of a function to the change in the input values over that interval
Difference Quotient or Quotient of Differences - correct answers ✅ Degree of a Polynomial - correct answers ✅In standard form, the degree of the polynomial is the degree of the highest degreed term. In factored form, the degree of the polynomial is the sum of the degrees of each factor. Leading Coefficient of a polynomial - correct answers ✅In standard form, it is the coefficient of the term with the highest degree. In factored form, it is the product of all of the coefficients of each factor's highest degree term. Multiplicity - correct answers ✅If a linear factor (x-a) is repeated n time, the corresponding zero of the polynomial function has multiplicity n. Number of Complex zeros - correct answers ✅A polynomial of degree n has exactly n complex zeros when counting multiplicities. Real Zero - correct answers ✅If a is a real zero of a polynomial function p, then the graph of y=p(x) has an x- intercept at the point (a,0).