Questions and Answers
What is a relation?
What are the x and y coordinates of a point on the coordinate plane called?
ordered pair
What is the coordinate plane?
a plane formed by 2 perpendicular lines called axes
A function is a special relation where each x-value is paired with more than one y-value.
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What is the domain in a function?
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What is the range in a function?
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Define a variable.
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What is an independent variable?
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What is a dependent variable?
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What are other names for 'x'?
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What are other names for 'y'?
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A relation passes the vertical line test if a vertical line touches it only once.
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Define a discreet function.
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Define a continuous function.
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What does 'm' represent in the equation y = mx + b?
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What does 'b' represent in the equation y = mx + b?
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How does changing 'm' in the slope-intercept form affect the line?
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How does changing 'b' in the slope-intercept form affect the line?
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What is the linear parent function?
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Define slope.
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Why is slope important for linear equations and lines?
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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 x-intercept?
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What is the y-intercept?
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What is Direct Variation?
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What is Inverse Variation?
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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 a line of best fit?
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What is a system of equations?
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Study Notes
Relations and Functions
- A relation is a set of ordered pairs, defining a relationship between two variables.
- An ordered pair consists of x and y coordinates representing a specific point on the coordinate plane.
- The coordinate plane is formed by two perpendicular lines known as axes (x-axis and y-axis).
- A function is a relation where each x-value corresponds to a single y-value, passing the vertical line test.
Domain and Range
- The domain encompasses all possible x-values (inputs) in a function.
- The range includes all possible y-values (outputs) that correspond to the domain.
Variables in Functions
- A variable is a symbol (typically a letter) representing a number that can vary.
- The independent variable (x) is the input or cause in a function that can be controlled.
- The dependent variable (y) is the output or result that cannot be controlled, represented on one side of the equation.
Identifying Variables
- Other names for x include: domain, independent variable, and input.
- Other names for y include: range, dependent variable, and output.
Graphical Tests and Types of Functions
- The vertical line test determines if a relation is a function; a vertical line must touch the graph at only one point.
- Discrete functions display data as distinct points that can't be further divided (e.g., people).
- Continuous functions reveal data as a smooth curve, representing information that can be divided into smaller pieces (e.g., time).
Graphing Functions
- The graph of a linear function features a straight line, characterized by a constant slope.
- The graph of a quadratic function is a parabola opening upwards or downwards.
- The graph of an inverse function reflects that a variable decreases as another increases.
- Exponential decay graphs decrease rapidly initially and then level off.
- Exponential growth graphs increase rapidly, showing upward trends.
Slope-Intercept Form
- In the equation y = mx + b:
- "m" represents the slope, indicating the steepness of the line.
- "b" represents the y-intercept, the point where the line crosses the y-axis.
Slope Characteristics
- Adjusting "m" modifies the steepness of the line, while changing "b" moves the line vertically on the graph.
- The linear parent function is expressed as y = x.
Understanding Slope
- Slope is defined as the vertical change divided by horizontal change.
- For linear equations, slope remains constant throughout the line.
- A horizontal line has a slope of 0, while a vertical line has an undefined slope.
Intercepts
- The x-intercept is where the graph crosses the x-axis, represented as (x, 0).
- The y-intercept is where the graph crosses the y-axis, represented as (0, y).
Variations
- Direct Variation follows the equation y = mx, with a y-intercept at (0, 0).
- Inverse Variation is represented by y = 1/x, where as one variable increases, the other decreases.
Inequalities and Lines
- A linear inequality includes symbols like <, >, ≤, or ≥ in place of an equals sign.
- Parallel lines share the same slope, while perpendicular lines have slopes that are opposite and reciprocal (flipped fraction).
Additional Concepts
- A line of best fit is drawn on a scatterplot to represent the trend of the data.
- A system of equations comprises two or more equations plotted on the same coordinate plane.
Studying That Suits You
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Description
Prepare for the Algebra 1 End-of-Course exam with these flashcards. Each card covers key concepts such as relations, ordered pairs, and functions. Perfect for quick review and study before the test.
