Questions and Answers
What is a relation?
What are the coordinates of an ordered pair?
(x, y)
What is the coordinate plane?
A plane formed by 2 perpendicular lines called axes.
What defines a function?
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What does the domain of a function represent?
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What does the range of a function represent?
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What is an independent variable?
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What is a dependent variable?
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In the equation y = mx + b, 'm' stands for?
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In the equation y = mx + b, 'b' stands for?
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What happens to the slope when 'm' changes in slope-intercept form?
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What slope does a horizontal line have?
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What slope does a vertical line have?
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What is the point where the graph crosses the x-axis called?
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What is the point where the graph crosses the y-axis called?
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What is a linear inequality?
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How do the slopes of parallel lines compare?
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How do the slopes of perpendicular lines compare?
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What is the solution of a system of equations?
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What can a system with 2 equations have?
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How do you multiply exponents of like variables?
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How do you divide exponents of like variables?
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What does the term 'rate of change' refer to?
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What is the formula for compound interest?
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How do you solve proportions?
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What is the quadratic formula for solving quadratics?
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What represents the standard form of a line?
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What are perfect squares?
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Study Notes
Algebra Concepts and Definitions
- Relation: Set of ordered pairs.
- Ordered pair: Represents coordinates on a coordinate plane, written as (x, y).
- Coordinate plane: Formed by two perpendicular axes; x-axis runs horizontally and y-axis vertically.
- Function: A specific type of relation where each x-value has one unique y-value, passing the vertical line test.
- Mapping: Visual representation of x-values and their corresponding y-values.
- Table: A method to illustrate ordered pairs clearly.
Domain and Range
- Domain: The complete set of all possible x-values (inputs).
- Range: The complete set of all possible y-values (outputs).
Variables
- Variable: A letter/symbol that represents a numerical value (not a number itself).
- Independent variable: The controlled input variable (x).
- Dependent variable: The output variable that is influenced by the independent variable (y).
Functions and Their Characteristics
- Vertical line test: Determines if a relation is a function; if a vertical line touches the graph only once, it is a function.
- Discrete function: Graph displayed as individual points without connection.
- Continuous function: Graph depicted as a smooth curve.
Linear Functions
- Standard form: y = mx + b; where m = slope and b = y-intercept.
- Slope: Measures the steepness; calculated as rise over run (change in y/change in x).
- x-intercept: The point where the graph crosses the x-axis (x, 0).
- y-intercept: The point where the graph crosses the y-axis (0, y).
System of Equations
- System of equations: Consists of two or more equations/inequalities graphed on the same coordinate plane.
- Solution of a system: The point where the lines intersect or cross.
- Types of solutions: Can be no solution (parallel lines), one solution (intersection at one point), or infinitely many solutions (identical lines).
Quadratic Functions
- Quadratic equation: Involves 'x-squared' as the highest exponent.
- Solutions of a quadratic function: Found at x-intercepts, also known as roots or zeros.
Operations with Exponents
- Multiplying exponents: Add exponents for like bases.
- Dividing exponents: Subtract exponents for like bases.
- Zero exponent: Any non-zero number raised to the power of zero equals one.
Solving Inequalities
- Linear inequality: Involves inequalities (>, <, ≥, ≤) in place of an equal sign.
- Graphing inequalities: determines whether to use a solid/dotted line (closed/open) based on the inequality's inclusiveness.
Special Formulas
- Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a) for solving quadratic equations.
- Compound interest formula: A = P(1 + r/n)^(nt), accounting for the compounding period.
- Simple interest formula: I = PRT (interest = principal × rate × time).
Functions and Graphs
- Function notation: f(x) indicates the function, interchangeable with y.
- Increasing/Decreasing functions: Read graphs left to right to determine trends; upward indicates increasing, downward indicates decreasing.
- Axis of symmetry: For parabolas, represented by the line x = -b/(2a) in standard form.
Sequences and Patterns
- Arithmetic sequence: Sequence where each term increases by adding a constant.
- Geometric sequence: Sequence where each term increases by multiplying/dividing by a constant.
Correlation and Causation
- Correlation: Describes patterns among variables, range between -1 and 1 indicating strength/direction.
- Causation: Indicates one event causes another; not to be confused with correlation.
General Concepts
- Rate of change: Often synonymous with slope, representing how one variable changes in relation to another.
- Perfect squares: Result from multiplying integers by themselves (e.g., 1, 4, 9, 16...).
- Distinguishing functions: Linear functions increase at constant rates, while exponential functions increase at variable rates.
Important Terms
- Absolute value: The distance a number is from zero on the number line, disregard sign.
- Discriminant: In the quadratic formula, determines the nature of the roots: positive (two real solutions), zero (one real solution), negative (no real solution).
Studying That Suits You
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Prepare for your Algebra 1 End-of-Course (EOC) exam with these flashcards. Each card covers essential terms and concepts such as relations, ordered pairs, and functions. Perfect for quick reviews and mastering key algebraic ideas.