WGU C957 Applied Algebra Guide (Latest 2023/ 2024 Update) | Questions and Verified Answers| 100% Correct| Grade A

WGU C957 Applied Algebra Guide (Latest 2023/
2024 Update) | Questions and Verified Answers|
100% Correct| Grade A
Q: regression equation
Answer:
best fit equation for a set of real world data
Q: Concave up
Answer:
y = x^2
Q: Concave down
Answer:
y = -x^2
Q: inflection point
Answer:
a point where the concavity changes
Q: asymptote
Answer:
a line that continually approaches a given curve but does not meet it at any finite distance. A natural
limitation

Q: exponential function
Answer:
a function with 1 curve and asymptote
Q: logistic function
Answer:
function with 2 curves and 2 asymptotes

Q: Concave up parameters
Answer:
the function is increasing at an faster and faster rate
OR
the function is decreasing at a slower and slower rate
Q: concave down parameters
Answer:
the function is increasing at a slower and slower rate OR
the function is decreasing at a faster and faster rate
Q: quantitative variable
Answer:
a characteristic that can be measured numerically
Q: qualitative variable
Answer:
do not have a numerical value, but describe something;
colors, car model, political party, computer brands
Q: independent variable
Answer:
explains, influences, or affectsthe other variable;located on the x-axis of a graph
Q: dependent variable
Answer:
responds to the IV; located on the y-axis
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Constant e

2.71828

slope-intercept formula

y = mx + b

L + m

the upper limit of a logistic function equation

the lower limit of a logistic equation

rate of increase for a logistic equation

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

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

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

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

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