A2C Glossary

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Algebra 2 Connections Glossary

radian measure
	An arc of a unit circle equal to the length of the radius of the circle is one radian. The central angle for this arc has measure one radian. 1 radian = degrees. (p. 399)
range
	The range of a function is the set of possible outputs for a function. It consists of all the values of the dependent variable, that is every number that y can represent for the function f(x) = y . (pp. 18, 199)
ratio
	The comparison of two quantities or expressions by division. (p. 83)
rational number

rational equation
	A number that can be written as a fraction where a and b are integers and b ≠ 0. (p. 453)
	An equation that includes at least one rational expression. For example, . (p. 347)
rational expression
	An expression in the form of a fraction in which the numerator and denominator are polynomials. For example, is a rational expression.
rational function

real numbers
	A function that contains at least one rational expression. For example, .
	The set of all rational numbers and irrational numbers is referred to as the set of real numbers. Any real number can be represented by a point on a number line. (pp. 17, 199, 456)
rebound height
	The height a ball reaches after a bounce. (pp. 60, 64)

rebound ratio
	The ratio of the height a ball bounces after one bounce to the height from which it dropped. (pp. 60, 64)
reciprocal
	The multiplicative inverse of a number or an expression. (p. 682)
rectangular numbers
	The terms of the sequence 0, 2, 6, 12, 20, …. These numbers are called rectangular because they count the number of dots in rectangular arrays with the dimensions n(n + 1) where n = 0, 1, 2, 3, 4,...
recursive definition

reference angle
	For a sequence, a recursive definition is a rule that gives the first term and then tells us how to get the next term of the sequence from the term or terms that precede it. For example, in the Fibonacci sequence 1, 1, 2, 3, 5, 8, ... , the next term is the sum of the previous two terms.
	For every angle of rotation in standard position, the reference angle is the angle in the first quadrant whose cosine and sine have the same absolute values as the cosine and sine of the original angle. (p. 403)
reflect vertically
	Used here to mean reflect a graph across the x-axis so that every point (x, y) on the original graph becomes (x, −y)on the reflection. The graph of y = −x²is a vertical reflection of y = x². (p. 207)
relation

relative maximum (minimum)
	Functions are also relations, but relations are not necessarily functions. The equations for parabolas, ellipses, hyperbolas, and circles are all relations but only the equations that describe vertically oriented parabolas are functions. (pp. 6, 199)
	A function that has a “peak” (or “valley”) at a point P is said to have a relative maximum (minimum) at the point P. This is the point where the function changes direction.
remainder
	When dividing polynomials in one variable, the remainder is what is left after the constant term of the quotient has been determined. The degree of the remainder must be less than the degree of the divisor. In the example below the remainder is . . (p. 472) Also see “quotient.”

repeated root
	A root of a polynomial that occurs more than once. The root r will occur as many times as (x − r) is a factor of the polynomial. (p. 446) See “double root” and “triple root.”
repetition
	An important criterion to consider when counting outcomes of an event. Whether an outcome can be repeated determines the number of alternatives that would include that outcome. For example: If A, B, and C are letters written on cards, the number of arrangements possible will be 3 · 2 · 1. But if you ask how many arrangements of A, B, and C could appear on a license plate, the answer will be 3 · 3 · 3 . Arrangements that involve repetition of a letter, such as AAA or CAC are counted when counting possible license plates. (pp. 523, 529)
reversing
	To reverse your thinking can be described as “thinking backward.” It sometimes means starting at the end of a problem and working backward to the beginning. It is useful to think this way when you want to undo a process or understand a concept from a new direction. Thinking about inverse functions involves reversing your thinking. Writing polynomials, given their zeros is another example. (pp. 263, 286)
rewrite

right-multiply
	To rewrite an equation or expression is to write an equivalent equation or expression. Rewriting could involve using the Distributive Property, following the order of operations, using properties of 0 or 1, substitution, inverse operations, Properties of Logarithms, or use of trigonometric identities. We usually rewrite in order to change expressions or equations into more useful forms or sometimes, just simpler forms. (pp. 68, 97, 101, 144, 222, 244)
	Since multiplication of matrices is not commutative the product AB may not equal BA. If we want the product BA we can right‑multiply matrix B by matrix A or we can left‑multiply matrix A by matrix B. The order of the multiplication matters; therefore, we specify whether we are left‑multiplying or right‑multiplying. See “left-multiply.” (p. 366)
right angle
	An angle with measure 90º.
right triangle

roots of a function
	A triangle with a right angle.
	The number r is a root (or zero) of the function f(x) if f(r) = 0. A root may be a real or a complex number. Real roots occur where the graph of the function f(x) crosses the x-axis. Complex roots must be found algebraically. (pp. 144, 446, 447)
rule
	An algebraic representation or a written description of a mathematical relationship. (pp. 123, 135)