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45 Cards in this Set

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  • Back
What are the four ways to represent a function?
tables, graphs, words and models
In a table..is the independent variable on top or the bottom and where is the dependent variable?
independent variable is on top, dependent variable is on bottom
Which is the IV and the DV? input or output
Independent variable is input
Dependent variable is the output
When writing a sentence how do you construct one?
list when, where why and how many
What are the 4 parts of a model?
equation, output units and description, input units and description and input range
What is the definition of a function?
a relationship that assigns to each input exactly one output
What are variable costs? give ex.
costs that change from period to period. ex. utility bill, overtime
what are fixed costs? give an ex.
costs that do not vary or change, rent salaries
What is the average cost?
the total cost divided by the number of units produced
What is the revenue?
total money coming in price=quantity divided per unit
What is the profit?
revenue-total cost
What is the break even point?
profit=0, revenue=total cost
What is end behavior?
what the output (vertical) of the function at extreme ends (right or left)
What is a horizontal asymptote?
imaginary line that the output approaches as either the left or right end behavior (extreme end).
What is continuity?
a function is continuous on an open interval if the output of the function is defined at every point on the interval and there are no breaks or jumps in the output of the fucntion.
What is an exponential function?
output is the result of multiplying the previous output by a constant
What does 'r' stand for in the interest formula?
interest rate, annual percentage rate that must be in a decimal
What does the 'n' stand for in the interest formula?
number of times interest is compounded over a year
What does the 't' stand for in the the interest formula?
number of years money is left in account has to be written in years
In an interest formula what is the formula if the model is continuous with discrete interpretation, and what is it if it is continuous without restriction?
A=P (1 + r/n) ^nt
A(t)= Pe^rt
What does the 'e' stand for in the interest formula?
e^x
What is a linear function?
a function that repeatedly and at even intervals adds or subtracts the same value to the output.
What is the form of the linear function?
f(x)=ax + b
What does 'b' stand for in the linear function?
its the starting value, the output when the input is (0), vertical intercept, y-intercept
What does 'a' stand for in the linear function?
its the incremental change per unit of imput, rate of change, output changes by (a) units per every one input, slope
What is the slope?
a particular point is a measure of how quickly the output is changing as the imput changes at that point
What is the rate of change
slope
What helps to distinguish a linear function?
it has a constant rate of change (slope)
What are the characteristics of a table of a linear function?
the first differences will be constant or near constant, the scatterplot of the data will lack concavity
What is interpolation?
using your model to calculate new output values for input values within your given data set. reliable estimates
What is extrapolation?
using your model to calculate new output values for input values outside your given data set. less reliable estimates
What is the percent change formula?
(b-1*100%=percent change
What is 'a' in an exponential function?
the starting value
When is the exponential function increasing or decreasing?
when b>1 it is increasing, when 0<b<1
What are the characteristics of an exponential function?
concaves up, constant percent change, and an horizontal asymptote along the input axis
If there is a percent in the model then it tells you that it is what type of model?
an exponential model
What is a logarithmic function?
it is an inverse of an exponential function
What is the logarithmic equation?
f(x)=a+bln(2)
If 'b' is less than zero or higher than zero is it decreasing or increasing?
when it is less than zero it is decreasing, when it is higher than zero it is increasing
What are the characteristics of a logarithmic function?
one type of concavity, not defined for negative or zero input, has a vertical asymptote along output axis, initially characterized by fast growth or decline, eventually characterized by slow growth or decline
What is a logistic function?
it is used when the model changes exponentially with bounds.
What is the logistic function formula?
f(x)= L
----
1+ae^-bx
By looking at a graph of a logistic function how can you tell if it is increasing or decreasing?
if it is increasing then it will look like an "s" if it is decreasing then it will look like a backward 2.
When 'b' is increasing in a function or decreasing in a function what is approaching and what will be visible in the equation during each one?
'b' is more than zero it is increasing and approaching the limit L, when it is decreasing it is less than zero and approaching the lower limit 0, no negative sign will show with a decreasing function and a negative sign will show with an increasing function
What are the characteristics of logistic functions?
two types of concavity (it has an inflection point-where a change in concavity occurs), has two horizontal asymptotes, Y=L and y=0