Functions

Question Answer
variable symbol that can be replaced by any member of a set of numbers or objects
algebraic expression The result when numbers and variables are combined using the operations of arithmetic.
Order of Operations 1. Perform operations in parentheses, brackets.
2. Take powers.
3. Multiply and divide in order from left to right
4. add and subtract in order from left to right.
What is the dependent variable in the equation P=5H and why? P because its value depends on the amount for H. (H is independent variable)
Function A correspondence or pairing between 2 variables such that each value of the first (independent) variable corresponds to exactly one value of the second(dependent) variable.
Range of a Function The set of values of the dependent variable that can result from the substitutions for the independent variable.
Domain of a function the set of values which are allowable substitutions for the independent variable
How is f(x) read? "f of x"
How is T:x–> x read? "T maps x onto x." (arrow notation)
Theorem (Vertical-Line Test for Functions) No vertical line intersects the graph of a function in more than one point.
How do you "clear" an equation of fractions? Multiply each side of the equation by a common multiple of the denominator.
How do you simplify equation d= rt? multiply both sides by r. d/r = rt/r. Simplify d/r = t.
What is an explicit formula for the nth term of the sequence 1, 3, 6, 10, 15, 21, . . . ? t(n) = n(n+1)/2
What does a recursive formula state? a. The first term
b. tells how the nth term is related to one or more of the previous terms.
What are explicit formulas good for that recursive formulas are not? Explicit formulas help to find an answer for a large integer.
What are recursive formulas good for that explicit formulas are not? Recursive formulas help to find a series of numbers.

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