Algebra 1 NJ-SLA Math Vocabulary Flashcards

Questions and Answers

What is an equation?

A mathematical sentence that contains an equals sign and shows that two statements are the same.

What is an expression?

A mathematical phrase that contains operations, numbers, and/or variables, and does not have an equal sign.

What is an inequality?

A mathematical sentence that shows the relationship between quantities that are not the same, containing the symbols <, ≤, ≥, or ≠.

What kind of circle and arrow would a < (less than) inequality have when graphing?

Open circle with arrow to the left. Signup and view all the answers

What kind of circle and arrow would a ≥ (greater than or equal to) inequality have when graphing?

Closed circle with arrow to the right. Signup and view all the answers

What are rational numbers?

All positive and negative integers, fractions, and decimal numbers. Signup and view all the answers

What are integers?

The set of whole numbers and their opposites {...-2, -1, 0, 1, 2...}. Signup and view all the answers

What are integers greater than or equal to zero?

All positive whole numbers. Signup and view all the answers

What are rational numbers greater than or equal to zero?

All positive integers, fractions, and decimal numbers. Signup and view all the answers

What is the domain of a function?

All the possible x-values of a function. Signup and view all the answers

What is a function?

Each x value only correlates to one y value, and the x values do not repeat themselves (Vertical Line Test). Signup and view all the answers

What does f(x) stand for?

y. Signup and view all the answers

If given f(3), what should you do?

Substitute 3 in for x. Signup and view all the answers

If given f(x)=3, what should you do?

Substitute 3 in for y. Signup and view all the answers

What are real numbers?

All numbers, rational and irrational. Signup and view all the answers

What is a linear function?

An equation whose graph is a straight line, in which the highest exponent is 1. Signup and view all the answers

What is an increasing function?

Graph that increases from left to right. Signup and view all the answers

What is a decreasing function?

Graph that decreases from left to right. Signup and view all the answers

What are solutions to an equation?

Ordered pairs that make a true statement when plugged into the original equation, points that lie on the graph of a function. Signup and view all the answers

What is an x-intercept?

Where the graph crosses the x-axis, where y = 0. Signup and view all the answers

What is a y-intercept?

Where the graph crosses the y-axis, where x = 0. Signup and view all the answers

How do you find the x-intercept of an equation algebraically?

Substitute y = 0 and solve for x. Signup and view all the answers

How do you find the y-intercept of an equation algebraically?

Substitute x = 0 and solve for y. Signup and view all the answers

What is the rate of change?

Describes how a quantity is changing over time in any function, same formula as slope. Signup and view all the answers

What is slope?

Rise over run of a linear function. Signup and view all the answers

What does the graph of an equation of the form x = # look like?

Vertical line. Signup and view all the answers

What does the graph of an equation of the form y = # look like?

Horizontal line. Signup and view all the answers

What button(s) do you press on your calculator to graph an equation?

[ y = ], type the equation, then [graph]. Signup and view all the answers

What button(s) do you press on your calculator to look at a table after you've typed the equation?

[2ND] [GRAPH]. Signup and view all the answers

What button(s) do you press on your calculator to create a fraction?

[÷]. Signup and view all the answers

What button(s) do you press on your calculator to change a decimal to a fraction?

[MATH] [ENTER] [ENTER]. Signup and view all the answers

Where is the solution to a system of equations on a graph?

The point of intersection. Signup and view all the answers

What is a system of equations?

Two or more equations, with two or more variables, that are solved together. Signup and view all the answers

What is a system of inequalities?

A set of two or more inequalities with the same variables. Signup and view all the answers

Study Notes

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.

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Description

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!