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Questions and Answers
What is a function?
What is a function?
- The change in y over the change in x
- The space on an axis between two points
- A point on a graph
- A relationship between two variables (correct)
What does the domain refer to?
What does the domain refer to?
All the possible values of x
What does the range refer to?
What does the range refer to?
All the possible values of y
What is the x-intercept?
What is the x-intercept?
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What is the y-intercept?
What is the y-intercept?
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What is the slope?
What is the slope?
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What is the average rate of change?
What is the average rate of change?
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What is a zero slope?
What is a zero slope?
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What does a positive slope indicate?
What does a positive slope indicate?
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What does a negative slope indicate?
What does a negative slope indicate?
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What does an undefined slope indicate?
What does an undefined slope indicate?
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What is a discrete graph?
What is a discrete graph?
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What is a continuous graph?
What is a continuous graph?
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What is an interval in graphing?
What is an interval in graphing?
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Study Notes
Function and Variables
- A function defines a relationship between two variables, typically represented as x and y.
Domain and Range
- The domain consists of all possible x values that can be input into a function.
- The range encompasses all possible y values that can result from the function.
Intercepts
- The x-intercept indicates where a line intersects the x-axis, expressed as (x, 0).
- The y-intercept signifies where a line meets the y-axis, expressed as (0, y).
Slope Concepts
- Slope is determined by the ratio of the change in y (rise) to the change in x (run).
- A zero slope indicates a horizontal line where y remains constant across values of x.
- A positive slope shows that as x increases, y also increases, represented by an upward line from left to right.
- A negative slope indicates that as x increases, y decreases, represented by a downward line from left to right.
- An undefined slope occurs with a vertical line where x remains constant.
Rates of Change
- The average rate of change measures the slope between two distinct points on a curve, highlighting the overall trend.
Graph Types
- A discrete graph features individual points that are not connected, such as whole numbers or distinct time intervals.
- A continuous graph has connected points that form a line or curve, representing smooth transitions without interruption.
Intervals
- An interval describes the section on an axis between two specific points, utilized to identify ranges or sections within a graph.
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