Questions and Answers
What is a relation?
Set of ordered pairs.
What is an ordered pair?
The x and y coordinates of a point on the coordinate plane (x,y).
What is a coordinate plane?
A plane formed by 2 perpendicular lines called axes.
What is a function?
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What is a mapping?
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What is a table in terms of ordered pairs?
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What is the domain?
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What is the range?
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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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What is the vertical line test?
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What is a discrete function?
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What is a continuous function?
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In the equation y = mx + b, what does 'm' stand for?
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In the equation y = mx + b, what does 'b' stand for?
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What happens when you change the 'm' in the slope-intercept form of a line?
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What happens when you change the 'b' in the slope-intercept form of a line?
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Define slope.
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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 a linear inequality?
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How do you combine like terms?
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What is the 'rate of change' on a graph?
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What is the range in terms of data sets?
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When do you use a solid line and closed circle?
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Solve the literal equation R = A - P/T.
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When do you flip an inequality symbol?
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Are y= and f(x)= the same?
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How to solve function notation?
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What is another name for slope?
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What is the slope-intercept form?
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What is the point-slope form?
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What is the standard form of a line?
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Study Notes
Relations and Functions
- A relation consists of a set of ordered pairs.
- An ordered pair represents the coordinates of a point in the format (x, y).
- The coordinate plane is defined by two perpendicular axes: the x-axis (horizontal) and y-axis (vertical).
- A function is a specific type of relation where each x-value corresponds to only one y-value, ensuring no x-values repeat; verified through the vertical line test.
Variables and Terminology
- The domain includes all possible x-values (inputs).
- The range includes all potential y-values (outputs).
- The independent variable (x) represents the input or cause, while the dependent variable (y) illustrates the output or result.
- Other terms for x include domain, independent variable, and input. Alternative terms for y include f(x), range, dependent variable, and output.
Graphing and Slope
- Use the vertical line test to determine if a relation is a function: a vertical line must intersect the graph once.
- A discrete function is depicted as separate points on a graph, while a continuous function appears as a smooth curve.
- The slope measures a line's steepness, calculated as vertical change/horizontal change (rise over run); it can also indicate the rate of change.
Line Characteristics
- In the equation y = mx + b:
- "m" denotes the slope.
- "b" indicates the y-intercept.
- Changing "m" alters the line's steepness, while altering "b" moves the line up or down the y-axis.
- A horizontal line has a slope of 0; a vertical line has an undefined slope.
Intercepts and Inequalities
- The x-intercept is where the graph crosses the x-axis, with coordinates (x, 0).
- The y-intercept is where the graph crosses the y-axis, with coordinates (0, y).
- A linear inequality contains inequalities (<, >, ≤, or ≥) instead of an equation.
Combining Terms and Solving
- Combine like terms by adding their coefficients.
- For inequalities, flip the inequality symbol when multiplying or dividing by a negative number.
- When solving in function notation, substitute the x-value in the function and solve accordingly.
Equation Forms
- Slope-intercept form of a line: y = mx + b.
- Point-slope form: (y - y) = m (x - x)**; used to graph when both slope and a point are known.
- The standard form of a line is given by Ax + By = C, requiring no fractions or decimals, with A being positive.
Additional Concepts
- Rate of Change is synonymous with slope and is often referenced in word problems.
- When determining range from a data set, order values from smallest to largest and subtract the smallest from the largest to find the range.
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Description
Test your knowledge of relations and functions with this quiz. You'll explore concepts like ordered pairs, domain, and range, as well as the distinction between independent and dependent variables. Challenge yourself to apply the vertical line test and understand how to graph these mathematical principles.
