College Algebra Definitions Chapter 1 – Flashcards
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Unary Operation
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A unary operation is a calculation involving one operand.
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Binary Operation
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A binary operation is a calculation involving two operands.
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Operand
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An operand is a mathematical object upon which an operator acts.
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Binary Relation
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A binary relation is a comparison of two operands.
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Equation
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An equation is a mathematical statement which contains an = symbol.
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Identity
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An identity is an equation which is true for every real number in the domain of the variables.
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Conditional Equation
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A conditional equation is an equation which is true when some real numbers are substituted for the variables and is false when some real numbers are substituted for the variables.
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Contradiction
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A contradiction is an equation that has no real number solution.
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Solution
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A number (or numbers) that makes an equation true when substituted for the variable (or variables) is called a solution of the equation.
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Solution Set
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The collection of all solutions of an equation is called the solution set of the equation.
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Graph
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The graph of an equation consists of all the points, and only those points, whose coordinates are solutions of the equation.
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Graph
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An alternate, but equivalent definition is: The graph of an equation consists of all the points, and only those points, which satisfy the equation.
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Solving
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The process of finding all the solutions (the solution set) of an equation is called solving the equation.
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Equivalent Equations
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Two equations are equivalent if they have the same solution sets.
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Simplest Equation
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A simplest equation is an equation which has a single variable on one side of the equal sign and a single number on the other side.
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Linear Equation
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A linear equation in one variable is an equation that can be written in the form ax + b = 0 where a and b are real numbers with not both a and b equal to zero.
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Inequality
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An inequality is a mathematical statement which contains an inequality symbol.
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Solution of an Inequality
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A number (or numbers) that makes an inequality true when substituted for the variable (or variables) is called a solution of the inequality.
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Solution Set of an Inequality
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The collection of all solutions of an inequality is called the solution set of the inequality.
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Graph of an Inequality
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The graph of an inequality consists of all the points, and only those points, whose coordinates are solutions of the inequality.
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Graph of an Inequality
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An alternate, but equivalent definition is: The graph of an inequality consists of all the points, and only those points, whose coordinates satisfy the inequality.
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Equivalent Inequalities
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Two inequalities are equivalent inequalities if they have the same solution sets.
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Simplest Inequality
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A simplest inequality is an inequality which has a single variable on one side of the inequality symbol and a single number on the other side.
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Quadratic Formula
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The solutions of a quadratic equation are given by the above formula where a, b and c are the coefficients of the quadratic equation.
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Quadratic Equation in One Varaible
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A quadratic equation in one variable is an equation which may be written in the form ax² + bx + c = 0 where a, b, and c are real numbers and a is not zero.
