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Half the difference between the minimum and maximum values of the range. Only periodic functions with a bounded range have an amplitude. Essentially, amplitude is the radius of the range.
Analysis of a Function
An investigation based on the properties of numbers.
A sequence which has a constant difference between terms.
- e.g. 1, 5, 9, 13, 17 or 12, 7, 2, –3, –8, –13, –18
A data display that shows the five-number summary.
- Note: Not to be confused with box and whisker plots.
An official periodic count.
- An angle in a circle with vertex at the circle's center.
The difference between any two consecutive terms in an arithmetic progression.
The ratio of a term to the previous term.
e.g. The geometric series 3, 6, 12, 24, 48, . . . has common ratio r = 2.
Generally, there is only one event B such that A and B are both mutually exclusive and exhaustive; that event is the complement of A.
- e.g. A coin is flipped and one assumes it cannot land on its edge. It can either land on "heads" or on "tails" Because these two events are complementary, we have:
A probability that is computed based on the assumption that some event has already occurred. The probability of event B given that event A has occurred is written P(B|A).
The result of writing sum of two terms as a difference or vice-versa.
Note: Conjugates are similar to, but not the same as, complex conjugates.
A chart on which observed values of a variable are plotted.
The trig function cosecant, written cscθ. Cscθ equals 1 over sinθ.
The trig function cotangent, written cotθ. Cotθ equals 1/ tanθ or cosθ/ sinθ.
Angles which, drawn in standard position, share a terminal side.
e.g. 60°, -300°, and 780° are all coterminal.
A unit used to express the intensity of a sound wave.
A fixed reference line, situated on the convex side of a conic section, that is used when defining or calculating its eccentricity.
A point at which the graph of a relation or function is not connected.
To multiply out the parts of an expression.
- e.g. 3x(x + 8) = 3x·x + 3x·8
- = 3x2 + 24x
An alternative to a bar chart or line graph. Each value is recorded as a dot, so that the frequencies for each value can easily be counted.
e≈ 2.7182818284... is a transcendental number encountered when working with exponential models and exponential functions. e is also the base of the natural logarithm.
A conic section which is essentially a stretched circle.
- formula: distance[P,F1] + distance[P,F2] = 2 a, where a is a positive constant.
For polynomials, the end behavior is indicated by drawing the positions of the arms of the graph, which may be pointed up or down.
Experimental probability of an event is the ratio of the number of times the event occurs to the total number of trials.
A study in which conditions are under the direct control of the investigator.
A formula that allows direct computation of any term for a sequence.
Exponent Rules & Properties
- 1. an = a·a·a···a (n times)
- 2. a0 = 1 (a ≠ 0)
- 3. a-n= 1/an (a ≠ 0)
- 4. am/n= n \/---am or (n\/---a)m (a ≥ 0, m ≥ 0, n > 0)
- 1. multiplication: axay = ax + y
- 2. division: ax/ay=ax-y (a ≠ 0)
- 3. powers: (ax)y = axy
- Distributing (a ≥ 0, b ≥ 0)
- 1. (ab)x = axbx
- 2. (a/b)x = ax/bx (b ≠ 0)
- 1. (a + b)n ≠ an + bn
- 2. (a – b)n ≠ an – bn