1-1: The Language of Algebra.
1-2: What is a Function?
1-3: Function Notations.
1-4: Graphs of Functions.
1-5: Solving Equation.
1-6: Rewriting Formulas.
1-7: Explicit Formulas for Sequences.
1-8: Recursive Formulas for Sequences.
1-9: Notation for Recursive Formulas, Projects, Summary and Vocabulary, Progress Self-test, Chapter Review.
The Language of Algebra.
The language of Algebra uses numbers and variables. A variable is a symbol that can be replaced by any menber of a set of numbers or other objects. When numbers and variables are combibed using the operations of arithmetic, the result is called an algebraic expression, or simply an expression.
The expression π r ^ 2 uses the variable r and the numbers π and 2. An algebraic expression with two variables is a + b.
An algebraic sentence consists of expressions related with a verb. The most common verbs in algebra are = ( is equal to ), < ( is less than ), > ( is greater than ), ≤ ( is less than or equal to ), ≥ ( is greater that or equal to ), ≠ ( is not equal to ), and ≈ ( is approximately equal to ). Some algebraic sentences are A = π r ^ 2, a + b = b + a, and 3x + 9 < 22.
Algebra is the study of expressions , sentences, and other relations involving variables. Because many expressions and sentences are based on patterns in arithmetic, algebra sometimes is called generalized arithmetic.
Writing Expressions and Sentences
From your earlier study of algebra, you should know how to write expressions and sentences describing real situations, and how to evaluate expressions or sentences.
Express the cost of y cans of orange juice at x cents per can.
Use a special case. 5 cans at 60¢ per can would cost 5 * 60¢ = $3.00. That suggests multiplication. So y cans at x cents per can will cost xy cents.
Recognize a general model for multiplication. The unit " cents per can, " which can be written as...