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# Chapter 1

### Functions

A VARIABLE is a symbol that can be replaced by any number of a set of numbers or other objects. EX: x,y,w,r, etc.
An ALGEBRAIC EXPRESSION, or simply an EXPRESSION, is the result of variables and numbers that combine using the order of operations of arithmetic EX: 3x+9, 4y*8x+16
AN ALGEBRAIC SENTENCE consists of expressions related with a verb ( =, <, >, etc.) EX: a+b = b+a, 3x+9<22
EXAMPLE: Kim collects stamps. She now has 9000 stamps. If Kim buys 40 stamps each month, how many stamps will she have after m months? ANSWER: Kim will have 9000+40m stamps after m months.
ORDER OF OPERATIONS 1) Parentheses (), brackets [], or toher grouping symbols, like square root symbols or fraction bars 2) Powers 3)Multiply and divide in order from left to right 4) Add and subtract in order from left to right
An EQUATION is a sentence staing that two expressions are equal. EX: A=(PIE)r^2, S= 2wl+2wh+2lh, a+b=a+b
A FORMULA is an equation stating that a single variable is equal to an expression with one or more different variab;es on the other side. EX: A=(PIE)r^2, S=2wl+2wh+2lh
In the equation P=5H, what is the DEPENDENT variable and what is the INDEPENDENT variable? P is the dependent because its value depends on the number of hours worked and H is the independent.
A FUNCTION is a correspondence or pairing between to variables sucj that each value of the first (ind.) variable corresponds to exactly one value of the second (dep.) variable. In P=5H each value that is sucstituted for H results in just one value of P, so the relationship by this equation is a function. P is a function of H.
The DOMAIN of a function is the set of values which are allowable substitutions for the independent variable. The substitutions for the independent variable are often called the INPUT. (usually x)
The RANGE of a function is the set of values of the dependent variable that can result from the sustitutions for the independent variable. The resulting values of the dependent variable are often called the OUTPUT. (usually y)
NATURAL NUMBERS or COUNTING NUMBERS 1,2,3,4,5,6,...
WHOLE NUMBERS 0,1,2,3,4,5,...
INTEGERS ...-3,-2,-1,0,1,2,3...
RATIONAL NUMBERS THe set of numbers that can be represented as ratios of the form a/b, where a and b are integers and b does not equal 0. EX: 0,1,-7,2/3,1 9/11,.34/10,.004,9.618
REAL NUMBERS The set of numbers that can be represented by decimals. EX: 0,1,-7, 35 million, 2.34, (PIE)
f(x) NOTATION The symbol is read "f of x"
ARROW (or MAPPING) NOTATION EX: T:x-> X, read "T maps x onto x"
A RELATION is any set of ordered pairs. Every function is a relation but not all relations are functions. Not all grpahs represent a function. EX:(x,y)
THEOREM (VERTICAL-LINE TEST for FUNCTIONS) NO vertical line intersecs the grapgh of a function in more than one point.
DISTRIBUTIVE PROPERTY For all real numbers a, b, and c, c(a+b)= ca+cb
OPPOSITE of a SUM THEOREM For all real numbers a and b, -(a+b)=-a+-b
A SEQUENCE is a function whose domain is the set of natural numbers or the natural numbers from 1 to n. EX: 40,20,10,5,2.5,...
A RECURSIVE FORMULA or RECURSIVE DEFINTION for a sequence is a set of statements that a) indicates the first term (or first few terms), and b) tells how the nth term is related to one or more of the previous terms. EX: 40,20,10,5,2.5,... first term=40 new term =previous term divided by 2 for all terms after the first
Created by: jessries0139