Questions and Answers
When is an equation with variables on both sides ready to solve?
When the variables are together and like terms are combined.
Infinite solutions is a true statement.
True
No solution is a false statement.
False
What is mapping in a relation or function?
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What is a relation?
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What is a function?
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What is the domain?
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What is the range?
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What is function notation?
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What is absolute maximum?
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What is the y-intercept?
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What is absolute minimum?
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What is relative maximum?
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What is relative minimum?
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What does the x-axis represent?
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What does the y-axis represent?
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A continuous graph has points that are connected.
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A discrete graph has points that are not connected.
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Growth means that as X increases, Y decreases.
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Decay means that as X increases, Y decreases.
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What is slope?
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What is the slope formula?
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A negative slope indicates that a line goes up from left to right.
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A positive slope indicates that a line goes down from left to right.
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What does slope equal?
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A horizontal line has a slope that is always 0.
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A vertical line has an undefined slope.
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What is an explicit formula?
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What is a recursive formula?
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What is a common difference?
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What is the linear equations formula?
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What is the x-intercept?
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What does parallel mean in terms of lines?
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What does perpendicular mean in terms of lines?
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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 a one solution system of equations?
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What is an infinite system of equations?
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What is a no solution system of equations?
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Study Notes
Equations and Solutions
- An equation with variables on both sides is ready to solve when there are no parentheses, the variables are combined, and like terms are simplified.
- Infinite solutions exist when the equation is a true statement for all values.
- No solution occurs when an equation leads to a false statement.
Functions and Relations
- Mapping represents a relation or function visually, showcasing the input-output series.
- A relation consists of a series of input and outputs, while a function is a specific type of relation where each input corresponds to exactly one output.
- The domain includes all possible inputs, and the range encompasses all possible outputs.
Graphical Concepts
- Function notation provides an alternative way to express functions.
- The absolute maximum is the highest point on a graph, while the absolute minimum is the lowest point.
- Relative maximum and minimum refer to local peaks and valleys, respectively; they cannot be endpoints of a graph.
Axes and Graph Types
- The x-axis represents the independent variable (inputs, domain) while the y-axis represents the dependent variable (outputs, range).
- A continuous graph connects all its points, whereas a discrete graph features separate, unconnected points.
Growth and Decay
- Growth describes a situation where Y increases as X increases.
- Decay occurs when Y decreases as X increases.
Slope and Lines
- Slope is calculated using the formula Rise/Run or Y/X.
- The slope formula is expressed as (Y2 - Y1) / (X2 - X1).
- A negative slope indicates the line descends from left to right, and a positive slope indicates it ascends.
- A horizontal line has a slope of 0, while a vertical line has an undefined slope.
Sequences and Formulas
- An explicit formula is represented as an = a1 + d(n - 1).
- A recursive formula is expressed as an = an-1 + d.
- The common difference refers to adding or subtracting the same value repeatedly.
Linear Equations
- The standard form of a linear equation is Ax + By = C.
- The x-intercept is the point where the graph crosses the x-axis, resulting in Y being zero.
- Parallel lines maintain the same slope and never intersect, while perpendicular lines intersect at 90 degrees with opposite slopes.
Forms of Equations
- Slope-intercept form is given by Y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form is expressed as y - y1 = m(x - x1).
Systems of Equations
- A one-solution system is characterized by being constant and independent.
- An infinite system arises when the equations are constant and dependent.
- A no-solution system occurs when the lines are inconsistent, indicating they are parallel.
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Description
Test your understanding of key concepts in algebra, including equations with variables, functions, relations, and graphical representations. This quiz covers infinite and no solutions, function notation, and maximum values. Prepare to apply these concepts in various scenarios.