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A function can be represented by a list of ordered pairs. {(-1, 2), (-2, 3), (-3, 4), (-4, 5)} scalene triangle A triangle with no congruent sides. Scalene Not Scalene reflection A transformation that reflects, or “flips”, a graph or figure across a line, called the line of reflection. Line of reflection 6 5 4 G F 3 2 H 1 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 I -2 -3 -4 -5 -6 G' H' 1 2 3 4 5 I' F' 6 7 8 A function can be represented by a verbal description. Use words to describe the functional relationship. x -1 0 1 The y-values for a set of points are 4 more than twice the corresponding x-values. y 2 4 6 isosceles triangle A triangle with at least two congruent sides. opposite of a number The opposite of a number a, designated –a, is the number that is the same distance from zero as a, on the opposite side of the number line. The sum of opposites is 0. 3 -3 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 -3 is the opposite of 3 -3 + 3 = 0 6 7 8 9 square root A number that is multiplied by itself to form a product is called a square root of that product. Square root symbol: Ex: 5 x 5 = 25, so 25 = 5 translation • A translation is a transformation that shifts or “slides” every point of a figure or graph the same distance in the same direction. A' A B D B' C D' C' Quad ABCD Quad A’B’C’D’ A function can be represented by a graph. • Graph the ordered pairs and the line that contains them. x y -2 -7 -1 -5 0 -3 1 -1 2 1 domain The set of all values of the independent variable or all the x-coordinates in a function’s ordered pairs. Ex: {(0, 1), (2, 5), (3, 6), (4, 9)} Domain: {0, 2, 3, 4} dilation • A transformation that is a proportional enlargement or reduction of a figure through a point called the center of dilation. • Scale factor - Size of enlargement or reduction • An enlargement has a scale factor > 1. y The origin is the center of dilation. 9 8 B' 7 6 5 4 A' A -9 -8 -7 -6 -5 -4 -3 -2 -1 3 2 1 -1 -2 -3 -4 -5 B 1 2 3 4 5 6 7 8 9 C C' -6 -7 -8 -9 Triangle ABC is transformed into triangle A’B’C’ by the dilation using scale factor of 2 x range The set of all values of the dependent variable or all the y-coordinates in a function’s ordered pairs. Ex: {(0, 1), (2, 5), (3, 6), (4, 9)} Range: {1, 5, 6, 9} A function can be represented by a table. f(x) = -2x + 3 x -1 0 1 2 y 5 3 1 -1 midpoint of a line segment Point that lies halfway between the segment’s endpoints and divides it into two congruent parts y To find the midpoint, find the average of the coordinates of the endpoints of the line segment 6 4 4 + ( 2) , 2 2 M(-1 , 1) 9 8 7 A(-6, 4) M(-1, 1) -9 -8 -7 -6 -5 -4 -3 -2 -1 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 1 2 3 4 5 6 7 8 B(4, -2) 9 x probability • Probability is a measure of how likely an event is to occur. • Probability of an event occurring must be from 0 to 1. 3 Ex: A number cube has faces numbered from 1 to 6. The probability of rolling an odd 5 3 1 = number is 3 out of 6, or . 6 2 1 Simplifying expressions • Simplifying expressions uses commutative, associative, and distributive properties to remove parentheses and combine like terms. • Like terms in an algebraic expression can be combined. • Remember that the expressions m2 and 1m2 are equivalent. Simplify the expression: m2 + 5 – 5m2 – 1. m2 + 5 – 5m2 – 1 = (1m2 – 5m2) + (5 – 1) m2 + 5 – 5m2 – 1 = –4m2 + 4 Prism • Three dimensional figure with two bases that are congruent polygons and faces that are rectangular polygons, called lateral faces. • Prisms are named by the shape of their base. Triangular Prism Lateral face Base Net of a three-dimensional figure • A two dimensional drawing that shows what a figure would look like when opened up and unfolded with its surfaces laid out flat. Triangular Prism Net for Triangular Prism translation A transformation that shifts or “slides” every point of a figure or graph the same distance in the same 6 direction. G FGH is translated 5 units to the right and 3 units down to F’G’H’. 5 4 F 3 H -8 -7 -6 -5 -4 -3 -2 2 G' 1 F'-10 -2 -3 -4 -5 -6 1 2 3 4 5 H' 6 Cylinder Three-dimensional figure with two congruent circular bases and a curved surface Base Curved surface Base dilation • A transformation that is a proportional enlargement or reduction of a figure through a point called the center of dilation • A reduction has a scale factor < 1. y The origin is the center of dilation. 9 8 7 6 5 4 3 2 1 A A' -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 B' B C' 1 2 3 4 5 6 7 8 C -6 -7 -8 -9 Triangle ABC is transformed into triangle A’B’C’ by the dilation using scale factor of ½. 9 Cross product • One way to solve a proportion is to use the cross product. x 3 = 14 2 2 x =3 14 2x = 42 x = 21 Rational Numbers • Numbers that can be written as the a ratio of two integers, b , where b 0. • Integers are the set of all positive and negative whole numbers, and zero. Rational Numbers -7, 24%, 0.2, 0.3 25 5 Not Rational Numbers , 15 event An outcome or set of outcomes in a probability experiment. Examples: Flipping a coin and it landing on heads Rolling two number cubes, numbered 1 – 6 and getting ones on both cubes 1 5 3 1 4 2 axis of symmetry A line that divides a plane figure or a graph into two congruent reflected halves Also called line of reflection Axis of symmetry (line of reflection)