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- https://stats.libretexts.org/Under_Construction/Purgatory/Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.15%3A_Quadratic_Functions/3.15.06%3A_OptimizationOptimization can be applied to a broad family of different functions. However, in this section, we will concentrate on finding the maximums and minimums of quadratic functions. There is a large body o...Optimization can be applied to a broad family of different functions. However, in this section, we will concentrate on finding the maximums and minimums of quadratic functions. There is a large body of real-life applications that can be modeled by quadratic functions, so we will find that this is an excellent entry point into the study of optimization.
- https://stats.libretexts.org/Under_Construction/Purgatory/FCC_-_Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.15%3A_Quadratic_Functions
- https://stats.libretexts.org/Under_Construction/Purgatory/FCC_-_Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.17%3A_Rational_Functions/3.17.06%3A_Complex_FractionsIn this section we learn how to simplify what are called complex fractions that both the numerator and denominator are fraction problems in their own right, lending credence to why we refer to such a ...In this section we learn how to simplify what are called complex fractions that both the numerator and denominator are fraction problems in their own right, lending credence to why we refer to such a structure as a “complex fraction.”
- https://stats.libretexts.org/Under_Construction/Purgatory/Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.15%3A_Quadratic_Functions/3.15.02%3A_Vertex_FormOnce you have your quadratic function in vertex form, the technique of the previous section should allow you to construct the graph of the quadratic function. However, before we turn our attention to...Once you have your quadratic function in vertex form, the technique of the previous section should allow you to construct the graph of the quadratic function. However, before we turn our attention to the task of converting the general quadratic into vertex form, we need to review the necessary algebraic fundamentals.
- https://stats.libretexts.org/Under_Construction/Purgatory/FCC_-_Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.15%3A_Quadratic_Functions/3.15.05%3A_MotionIf a particle moves with uniform or constant acceleration, then it must behave according to certain standard laws of kinematics. In this section we will develop these laws of motion and apply them to ...If a particle moves with uniform or constant acceleration, then it must behave according to certain standard laws of kinematics. In this section we will develop these laws of motion and apply them to a number of interesting applications.
- https://stats.libretexts.org/Under_Construction/Purgatory/FCC_-_Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.16%3A_Polynomial_Functions/3.16.02%3A_Zeros_of_PolynomialsIn the previous section we studied the end-behavior of polynomials. In this section, our focus shifts to the interior. There are two important areas of concentration: the local maxima and minima of th...In the previous section we studied the end-behavior of polynomials. In this section, our focus shifts to the interior. There are two important areas of concentration: the local maxima and minima of the polynomial, and the location of the x-intercepts or zeros of the polynomial. In this section we concentrate on finding the zeros of the polynomial.
- https://stats.libretexts.org/Under_Construction/Purgatory/FCC_-_Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.17%3A_Rational_Functions/3.17.02%3A_Reducing_Rational_FunctionsThe goal of this section is to learn how to reduce a rational expression to “lowest terms.” Of course, that means that we will have to understand what is meant by the phrase “lowest terms.” With that ...The goal of this section is to learn how to reduce a rational expression to “lowest terms.” Of course, that means that we will have to understand what is meant by the phrase “lowest terms.” With that thought in mind, we begin with a discussion of the greatest common divisor of a pair of integers.
- https://stats.libretexts.org/Under_Construction/Purgatory/Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.17%3A_Rational_Functions/3.17.02%3A_Reducing_Rational_FunctionsThe goal of this section is to learn how to reduce a rational expression to “lowest terms.” Of course, that means that we will have to understand what is meant by the phrase “lowest terms.” With that ...The goal of this section is to learn how to reduce a rational expression to “lowest terms.” Of course, that means that we will have to understand what is meant by the phrase “lowest terms.” With that thought in mind, we begin with a discussion of the greatest common divisor of a pair of integers.
- https://stats.libretexts.org/Under_Construction/Purgatory/Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.14%3A_Absolute_Value_Functions/3.14.03%3A_Absolute_Value_EquationsBecause the point where the graph of y = a intersects the left-hand branch of y = |x| has y-coordinate y = a, the x-coordinate of this point of intersection is x = −a. Because the point where the grap...Because the point where the graph of y = a intersects the left-hand branch of y = |x| has y-coordinate y = a, the x-coordinate of this point of intersection is x = −a. Because the point where the graph of y = a intersects the right-hand branch of y = |x| has y-coordinate y = a, the x-coordinate of this point of intersection is x = a. Recall that for any real number x, the absolute value of x is defined as the distance between the real number x and the origin on the real line.
- https://stats.libretexts.org/Under_Construction/Purgatory/FCC_-_Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.13%3A_Linear_Functions/3.13.04%3A_The_Point-Slope_Form_of_a_LineIn the last section, we developed the slope-intercept form of a line (y = mx + b). The slope-intercept form of a line is applicable when you’re given the slope and y-intercept of the line. However, th...In the last section, we developed the slope-intercept form of a line (y = mx + b). The slope-intercept form of a line is applicable when you’re given the slope and y-intercept of the line. However, there will be times when the y-intercept is unknown.
- https://stats.libretexts.org/Under_Construction/Purgatory/Finite_Mathematics_-_Spring_2023/03%3A_Functions/3.03%3A_Piecewise-Defined_FunctionsIn preparation for the definition of the absolute value function, it is extremely important to have a good grasp of the concept of a piecewise-defined function.
