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Questions and Answers
What is the domain?
x-values (left and right)
What is the range?
y values (min and max)
What is interval notation?
Represents a set of real numbers with a pair of values that are its left (minimum) and right (maximum) boundaries.
How do you find the x-intercept?
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How do you find the y-intercept?
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What is the zero of a function?
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What is the x-intercept?
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What is the y-intercept?
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What is the maximum of a function?
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What is the minimum of a function?
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How do graphs and equations reveal information about a relationship between two quantities?
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What is a vertex?
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What is the axis of symmetry?
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What is reflection in terms of functions?
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What is a positive graph?
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What is a negative graph?
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Study Notes
Key Features of Functions
- Domain: Refers to all possible x-values that a function can take. It represents the left and right boundaries of the graph.
- Range: Represents the set of possible y-values, indicating the minimum and maximum heights of the function.
- Interval Notation: A mathematical notation that expresses a set of real numbers using a pair of values; the left boundary (minimum) and the right boundary (maximum).
- Finding X-Intercepts: To identify x-intercepts, set y equal to zero; the corresponding x-values are where the graph intersects the x-axis.
- Finding Y-Intercepts: To find y-intercepts, set x equal to zero; the resulting y-values are where the graph intersects the y-axis.
- Zero of a Function: The x-value(s) that make the function output zero (f(x) = 0); these values are crucial for understanding where the graph intersects the x-axis.
- X-Intercept: The specific x-coordinate of points where the graph crosses the x-axis.
- Y-Intercept: The specific y-coordinate of points where the graph crosses the y-axis.
Function Behavior
- Maximum: The highest point on the graph, indicating the transition from increasing to decreasing values.
- Minimum: The lowest point on the graph, indicating the transition from decreasing to increasing values.
- Graph and Equation Relationship: Graphs and equations illustrate how variables x and y are interconnected. Changes in x affect y, typically represented as y = f(x), depicting the function's rule of connection.
Additional Key Concepts
- Vertex: The apex or lowest point of a graph, significant in determining the function's overall shape.
- Axis of Symmetry: A line that divides the function into two identical halves, displaying symmetrical properties.
- Reflection: A transformation that flips points across a specified line, creating a mirror image of the original graph.
- Positive Graph: Portions of the graph that lie above the x-axis, indicating positive y-values.
- Negative Graph: Portions of the graph that lie below the x-axis, indicating negative y-values.
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Description
Test your knowledge on the key features of functions in Algebra 2, focusing on domain, range, and intervals. This quiz covers the essential definitions and concepts that will help you understand increasing and decreasing intervals effectively.