Algebra 3-4 Final Exam
test point
a point that when tested shows which side of the graph will be shaded (usually 0,0 but cannot be on the boundary line). If the test point makes the inequality true, then shade that side of the graph. If the test point makes the inequality false, the shade the other side of the graph.
constant
a quantity whose value does not change; i.e. the 5 in 2x+5
half - plane
a region on a graph on one side of a boundary line
function
a relation in which each element of the domain (x) corresponds with exactly ONE element in the range (y)... There are no cheaters!!
algebraic EQUATION
a statement that two expressions are equal; contains an equal sign
variable
a symbol, usually a letter, that represents one or more numbers
>
greater than
≥
greater than or equal to
<
less than
≤
less than or equal to
parallel lines
lines that do not intersect and have the SAME slope
perpendicular lines
lines that intersect at a 90 degree angle and have slopes that are OPPOSITE RECIPROCALS of each other (i.e. 1/5 and -5)
inverse operations
math processes that "undo" each other
integers
negative and positive whole numbers
rational numbers
numbers than can be converted into a fraction (.125, 1/3, -0.5)
irrational numbers
numbers that cannot be converted into a fraction (7.8956745....)
stretch
occurs to a graph when "a" is greater than 1
compress
occurs to a graph when "a" is less than 1
whole numbers
positive whole numbers including 0
function rule
represents an output value in terms of an input value in a direct variation, written y=kx
horizontal line
slope is 0
vertical line
slope is undefined
sum, more than, increased by
terms about addition
difference, less than, decreased by
terms about subtraction
like terms
terms that have the same variables raised to the same powers; i.e. 2 & 7 or 3x & 8x
opposite
the additive inverse (i.e. 5 and -5)
quotient
the answer to a division problem
product
the answer to a multiplication problem
axis of symmetry
the line that divides a figure into two parts that are mirror images; in y = a|x-h| + k the AOS = h or x=h
reciprocal
the multiplicative inverse (i.e. 5 and 1/5)
coefficient
the numerical factor in a term; i.e. the 3 in 3x
constant of variation
the ratio of the two variables in a direct variation; the k in y=kx where k=y/x
slope
the ratio of vertical change to horizontal change between points on a non-vertical line AKA Rise over Run
domain
the set of all inputs, or x-coordinates, of an ordered pair
range
the set of all output, or y-coordinates, of an ordered pair
vertical-line test
used on a graph to determine whether a relation is a function... If a vertical line passes through more that one point on the graph, the relation is NOT a function
absolute value
written |x| is the distance of x from zero on the number line; it is NEVER negative
point-slope form
y - y1 = m (x - x1) where m=slope and (x1,y1) = a point ; both x1 and y1 look opposite!
parent function
y = |x|, y = x, and y=x^2 ; the simplest form of a set of functions
slope-intercept form
y= mx + b where m=slope and b=y-intercept
transformation or translation
a change made to at least one of the values a, h, and k where y=a|x-h|+k; they include vertical shifts, horizontal shifts, and vertical stretches and compressions
boundary line
a line of an inequality that separates the coordinate plane into half planes.
direct variation
a linear function, y=kx, where k is the constant of variation
algebraic expression
a mathematical phrase that contains one or more variables
term
a number, a variable, or the product of a number and one or more variables
vertex
(h,k) when y=a|x-h|+k; h looks opposite
Standard form
Ax + By = C
reflection over the x-axis
also known as opening down or flipping; occurs when "a" is negative
linear equation
an equation for a LINE that can be written in standard form, slope-intercept form, or point-slope form
inequality
an equation using the symbols < or > ; does not have an = sign
relation
any set of ordered pairs
natural numbers
counting numbers starting at positive 1
