Algebra 1 NJ-SLA Math Vocabulary Flashcards

Vocabulary and Definitions

• Equation: A mathematical sentence with an equals sign that indicates two statements are equivalent.
• Expression: A mathematical phrase combining operations, numbers, and/or variables without an equals sign.
• Inequality: A mathematical sentence indicating a relationship between unequal quantities using symbols like <, ≤, ≥, and ≠.

Graphing Inequalities

• Less than (<) Inequality: Represented by an open circle and an arrow pointing left.
• Greater than or equal to (≥) Inequality: Depicted by a closed circle with an arrow pointing right.

Types of Numbers

• Rational Numbers: Includes all positive and negative integers, fractions, and decimal numbers.
• Integers: The set of whole numbers including their negatives: {..., -2, -1, 0, 1, 2, ...}.
• Non-negative Integers: All whole numbers greater than or equal to zero.
• Non-negative Rational Numbers: Includes all positive integers, fractions, and decimal numbers.

Functions and Their Properties

• Domain of a Function: Comprises all possible x-values for that function.
• Function: A relation where each x-value corresponds to one unique y-value, pass the Vertical Line Test.
• Notation f(x): Represents the y-value of the function corresponding to x.

Function Evaluation

• To find f(3): Substitute 3 for x in f(x).
• To find f(x)=3: Substitute 3 for y in the function.

Types of Numbers Continued

• Real Numbers: All numbers, encompassing both rational and irrational numbers.
• Linear Function: An equation producing a straight line graph, characterized by a maximum exponent of 1.

Function Behavior

• Increasing Function: A graph that rises from left to right.
• Decreasing Function: A graph that falls from left to right.

Solutions and Intercepts

• Solutions to an Equation: Ordered pairs that satisfy the original equation, represented graphically on the function's graph.
• X-Intercept: The point where the graph intersects the x-axis (y=0).
• Y-Intercept: The point where the graph intersects the y-axis (x=0).

Finding Intercepts Algebraically

• X-Intercept: Found by setting y = 0 and solving for x.
• Y-Intercept: Found by setting x = 0 and solving for y.

Additional Concepts

• Rate of Change: Indicates how a quantity changes over time, calculated with the same formula as slope.
• Slope: Defined as the ratio of rise to run in a linear function.

Graphing Techniques

• Graph of x = #: A vertical line representation.
• Graph of y = #: A horizontal line representation.

Calculator Functions

• Graphing an Equation: Press [y =], input the equation, and then hit [graph].
• Viewing a Table: After entering the equation, press [2ND] [GRAPH].
• Creating a Fraction: Use the division sign [÷].
• Converting a Decimal to a Fraction: Use [MATH] [ENTER] [ENTER].

Solving Systems

• Solution to a System of Equations: Identified at the point where the graphs intersect.
• System of Equations: Consists of two or more equations with common variables, solved simultaneously.
• System of Inequalities: Comprises two or more inequalities sharing the same variables.

Test your understanding of key vocabulary in Algebra 1 with these flashcards. Learn definitions such as 'equation', 'expression', and 'inequality' to enhance your mathematical language skills. Perfect for NJ-SLA students looking to solidify their knowledge!