WGU C957 Latest Update Already Passed

WGU C957 Latest Update Already Passed Constant e 2.71828 slope-intercept formula y = mx + b L + m the upper limit of a logistic function equation m the lower limit of a logistic equation k rate of increase for a logistic equation C start of increase for a logistic equation linear function that is a straight line polynomial function with curves and no asymptote 0.7-1.0 r^2-value showing a strong correlation 0.3-0.7 r^2-value showing a moderate correlation 0.0-0.3 r^2-value showing a weak correlation outlier a data point which is distinctly separate from all others within a data set for reasons beyond the data coefficient of determination rating how well the function fits the real world data r^2 coefficient of determination regression equation best fit equation for a set of real world data Concave up y = x^2 Concave down y = -x^2 inflection point a point where the concavity changes asymptote a line that continually approaches a given curve but does not meet it at any finite distance. A natural limitation exponential function a function with 1 curve and 1 asymptote logistic function function with 2 curves and 2 asymptotes Concave up parameters the function is increasing at an faster and faster rate OR the function is decreasing at a slower and slower rate concave down parameters the function is increasing at a slower and slower rate OR the function is decreasing at a faster and faster rate quantitative variable a characteristic that can be measured numerically qualitative variable do not have a numerical value, but describe something; colors, car model, political party, computer brands independent variable explains, influences, or affects the other variable; located on the x-axis of a graph dependent variable responds to the IV; located on the y-axis input independent variable output dependent variable function notation f(input) = output or f(x) = y inverse function a function that "undoes" what the original function does interval range of values brackets used to indicate an endpoint of an interval is included parentheses used to indicate an open endpoint in an interval Moore's Law about every 2 years, the number of transistors that can fir on a circuit doubles inverse function denotation f^-1(x) Order of Operations Parentheses, Exponents, Multiplication, Division, Addition, Subtraction linear function y = mx + b line's slope y = mx + b rate of change describes how a quantity is changing over time (per) y-intercept y = mx + b Multivariate involving multiple factors, causes, or variables temperature conversion C(F) = (F-32)/1.8 F(C) = 1.8C + 32 origin A fixed point from which coordinates are measured. (y, x) what is the inverse of (x, y) m = (y2-y1)/(x2-x1) slope formula linear function aspect always has the same rate of change ratio a comparison of two quantities starting values and slopes important aspects of linear functions slopes positive: lines that increase negative: lines that decrease scatterplot a graphed cluster of dots, each of which represents the values of two variables line of best fit a line drawn in a scatter plot to fit most of the dots and shows the relationship between the two sets of data least-squares regression algorithm used to find the best-fit line for the scatterplot regression line line of best fit correlation coefficient measures how closely the data values in a scatterplot follow the path of a straight line r-value correlation coefficient is a number between -1 and 1 that measures the strength and direction of a linear relationship r^2-value coefficient of determination; number between 0 and 1; is the appropriate measure for determining how well a particular function fits, or models the data always the same rate of change for a linear function polynomial function a function with real non-negative numbers - constants, variable, and exponents, that can be combined using addition, subtraction, multiplication, and division polynomial's degree variable's maximum exponent linear polynomial degree of 1 quadratic polynomial degree of 2 cubic Degree of 3 degree 1 polynomial cannot handle any turns; data must be increasing or decreasing, and must do so at a constant rate degree 2 polynomial can handle 1 turn in the data degree 3 polynomial can handle 2 turns in the data fourth-degree polynomial can handle 3 turns in the data linear polynomial function f(x) = ax + b Quadratic Polynomial function f(x) = ax^2 + bx + c Cubic polynomial function f(x) = ax^3 + bx^2 + cx + d Plug estimation into the equation how to check the accuracy of input estimate Solving a polynomial function - determine the output value you are looking for - start with the specific output, trace that value on the dependent variable axis to any associated coordinates on the graph - trace from these associated coordinates to their corresponding values on the independent variable axis - estimate these values check your solutions by plugging them back into the equation and verify you get the output value identified in the first step r^2 strength 0.7 - 0.1: strong model/correlation 0.3 - 0.7: moderate model/correlation 0 - 0.3: weak model/correlation 0: no model/correlation decrease general effect of outliers on the coefficient of determination average rate of change represents how 1 variable changes with respect to another over an interval of values instantaneous rate of change represents how 1 variable changes with respect to another at a particular instant when polynomials do not work forecasting the future; they are best for modeling data that has several ups and downs (or turns), but once past all the turns, they sometimes lose their power in modeling leading term the term in a polynomial which contains the highest power of the variable concavity function that increases over certain intervals and decreases over others concave up opens upward concave down opens downward constant ratio the previous amount is always multiplied by a fixed number to get to the next amount exponential function f(x) = Ca^x; where C is the initial amount and a is the common ratio exponential function what type of function is Moore's Law? exponential function has a constant ratio number e used frequently with exponential functions; a constant number real-life situations best modeled by exponential functions -compound interest -uninhibited growth -radioactive decay -heating or cooling objects percentage when an increase is expressed in this way, the situation automatically becomes exponential because it is a constant ratio porportionally how exponential functions grow; in general, in an exponential growth function f(x) = a X b^x, the growth rate b is based on the exponent limiting factors Asymptotes No asymptote linear function No asymptote polynomial function One asymptote exponential function 2 asymptotes logistic function logistic functions when data grows fast at first, then slows down and finally approaches a limit, this function should be used to model the data Logistic Function Equation C-value determines how quickly a logistic function starts to grow; the smaller the value, the quicker it grows Visually how to tell the steeper rate of change, which is the greater magnitude rate of change exponent number indicates how quickly a logistic function increases or decreases positive exponent indicates the quantity is decreasing in logistic functions