What Are They? What Are They ? Expressions What Are They ? Handling linear equations is a basic skill that all students of algebra should have. This module addresses what is required. Expressions 1/30/2013

What Are Expressions ? Algebraic Expression What Are They? Algebraic Expression A symbol, or finite combination of symbols, that represents a number Algebraic symbols represent constants, variables, arithmetic operations, functional values and grouping symbols Symbols are used for computation of expression value What Are Expressions ? Let us consider what we mean by an expression. In its simplest form, an expression represents a number, whose value is known only when all variables in the expression are given values. 1/30/2013 Expressions Expressions 1/30/2013

What Are Expressions ? Algebraic Expressions Constants Variables What Are They? Algebraic Expressions Constants Fixed values represented by real (or complex) numbers such as 2, 5, 6.98, or by symbols such as Variables A real (or complex) variable is an unknown real (or complex) number usually represented by letters such as x, y, m, n, k, etc. a, b, c, , or e What Are Expressions ? Let us consider what we mean by an expression. In its simplest form, an expression represents a number, whose value is known only when all variables in the expression are given values. 1/30/2013 Expressions Expressions 1/30/2013

What Are Expressions ? Algebraic Expressions Arithmetic Operations What Are They? Algebraic Expressions Arithmetic Operations Symbols +, – , • , and / (for Functional Values f(x), g(y), ex , x2 , log2 x , Groupings Paired symbols such as ( ), [ ] or { } Used to group expression symbols to indicate order of computation • )  x + 1 What Are Expressions ? Let us consider what we mean by an expression. In its simplest form, an expression represents a number, whose value is known only when all variables in the expression are given values. 1/30/2013 Expressions Expressions 1/30/2013

Expressions  Expression Examples 1. 17 2. a – b 3. 2x + 17 1. 17 2. a – b 3. 2x + 17 4. 3(x2 – 6)/(x – 2)3 5. 6. ((x + 1)2 – 5 log3 x)2 + 24y 7. [(x + 1)2 – 5 log3 x]2 + 24y  x + 5 4 – 3 1/30/2013 Expressions

Expressions What do we DO with expressions ? Simplify them What Are They? What do we DO with expressions ? Simplify them Evaluate them when variables are known We DO NOT solve expressions An expression represents a number, not a statement of equality or inequality Without further information we cannot find the value of any variable in the expression What Are Expressions ? Let us consider what we mean by an expression. In its simplest form, an expression represents a number, whose value is known only when all variables in the expression are given values. 1/30/2013 Expressions Expressions 1/30/2013

Expressions vs Equations What Are They? Expressions are NOT Equations Expressions vs Equations Expressions are merely strings of characters with no intrinsic value, especially no truth value. They are neither true nor false nor numerically equivalent to any number – at lease until values are provided for any variables and parameters in the expression. Equations are statements that are either true or false, depending on their content. Conditional equations containing variables may be solved for certain variable values that make the equation true. An algebraic equation is typically a statement of the equality of two expressions. The statement may be true or false for certain values of variables in the expressions. Note: We cannot solve an expression 1/30/2013 Expressions Expressions 1/30/2013

Expressions vs Equations What Are They? Expressions are NOT Functions Expressions vs Functions A function is defined in terms of its ordered pairs. An expression is defined as a string of characters and has no ordered pairs. Is there some connection between functions and expressions? It turns out that functions that have some algebraically expressed rule for determining range values from given domain values may use an expression to describe the rule. For example, if function f(x) is represented as f(x) = x2 + 1 then functional values (i.e. range elements) can be found by evaluating the expression x2 + 1 provided appropriate values of x (i.e. domain values) are given. Note: Functions have a domain and range but expressions do not 1/30/2013 Expressions Expressions 1/30/2013

Think about it ! What Are They? Expressions 1/30/2013 Expressions