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58 Cards in this Set
- Front
- Back
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rule of four
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functions can be represented by tables, graphs, formulas and descriptions
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what is a function
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a rule tht takes numbers as inouts and assigns each a def output
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domain
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input number
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range
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output numbers
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descrete functions
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only take certain values ex mon tues wed not mon and 1/2
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rule of four
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functions can be represented by tables, graphs, formulas and descriptions
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what is a function
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a rule tht takes numbers as inouts and assigns each a def output
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domain
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input number
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range
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output numbers
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descrete functions
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only take certain values ex mon tues wed not mon and 1/2
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continous functions
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takes rations, uses interval notation
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interval notation
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Interval notation is a method of writing down a set of numbers. Usually, this is used to describe a certain span or group of spans of numbers along a axis, such as an x-axis
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function notation
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A function is a rule that takes an input, does something to it,
and gives a unique corresponding output. There is a special notation, called "function notation," that is used to represent this situation: if the function name is f , and the input name is x , then the unique corresponding output is called f(x) (which is read as " f of x ".) |
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lines
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constant and average rates of change
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secant line
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A secant line of a curve is a line that (locally) intersects two points on the curve. The word secant comes from the Latin secare, to cut.
directly from one point to another |
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composite functions
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f (g(x)
s a mathematical expression which changes one number into another. It always changes a number the same way. A composite function is a combination of two functions, where you apply the first function and get an answer, and then fill that answer into the second function. |
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function shifts to the left and right
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y = f (x − c)
Shifts the graph right c units (add c to x-values) y = f (x + c) Shifts the graph left c units (subtract c from x-values) |
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functions shifts up and down
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1.1 y = f (x) + c
Shifts the graph up c units (add c to y-values) 1.2 y = f (x) − c Shifts the graph down c units (subtract c from y-values) |
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function stretching and compressing
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1/c*f(x)
c*f(x) |
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direct proportionality
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y=kx
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composite functions
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f (g(x)
s a mathematical expression which changes one number into another. It always changes a number the same way. A composite function is a combination of two functions, where you apply the first function and get an answer, and then fill that answer into the second function. |
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function shifts to the left and right
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y = f (x − c)
Shifts the graph right c units (add c to x-values) y = f (x + c) Shifts the graph left c units (subtract c from x-values) |
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functions shifts up and down
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1.1 y = f (x) + c
Shifts the graph up c units (add c to y-values) 1.2 y = f (x) − c Shifts the graph down c units (subtract c from y-values) |
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function stretching and compressing
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1/c*f(x)
c*f(x) |
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direct proportionality
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y=kx
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indirect proportionality
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y=k/x
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power function
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y=Kx^p
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leading term
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term of the highest degree, first term
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monomial
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polynomial with just one term
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steepness/ slope/ m
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changer in y/ change in x
magnitude of m |
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indirect proportionality
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y=k/x
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power function
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y=Kx^p
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leading term
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term of the highest degree, first term
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monomial
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polynomial with just one term
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steepness/ slope/ m
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changer in y/ change in x
magnitude of m |
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interpolation
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Interpolation is the process of obtaining a value from a graph or table that islocated between major points given, or between data points plotted. A ratioprocess is usually used to obtain the value.
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extrapolation
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Extrapolation is the process of obtaining a value from a chart or graph thatextends beyond the given data. The "trend" of the data is extended past the lastpoint given and an estimate made of the value.
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growth decay rates
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understand that an exponential function increases or decreases by a constant PERCENTAGE for each unit increase in the independent variable
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exponential functions have
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an increasing averg rates of change.. concave up
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changing the initial value (families of functions)
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as large values of a mean faster growth
values of a near o mean faster dacay |
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coninious growth decay
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uses e, doesnt add a 1 to the precentage, can use ln to get rid of e
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compound interest
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arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding (for example the interest is compounded).
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product rule
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m'n+mn'
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quotient rule
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nm'-mn'/
n^2 |
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log rules
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x mean +
/ mean - ln e^x equals ln e^x |
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natural log
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the power of e needed to get x
x=c it is e^c=x |
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instantaneous rate of change
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The rate of change at a particular moment. Same as the value of the derivative at a particular point
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2nd derivative
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related to concavity
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chain rule
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der of os X is X der of is
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riule of ln
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f(x)= lnx
f(x)= 1/x * x' |
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natural log
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the power of e needed to get x
x=c it is e^c=x |
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instantaneous rate of change
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The rate of change at a particular moment. Same as the value of the derivative at a particular point
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2nd derivative
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related to concavity
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chain rule
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der of os X is X der of is
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riule of ln
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f(x)= lnx
f(x)= 1/x * x' |
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critical point
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local max/min
inflection points |
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inflection point
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where it changes direction
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riemann sums
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upper lower left handed right handed overestimates and underestimates
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