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Questions and Answers
What is a Linear Function?
What is a Linear Function?
- A function that can be written in the form y = mx + b (correct)
- A non-linear function
- A constant function
- A type of quadratic function
What is the domain of a function?
What is the domain of a function?
The set of input values of a function.
What is the range of a function?
What is the range of a function?
The set of output values of a function.
The vertical line test is used to determine if a graph is a function.
The vertical line test is used to determine if a graph is a function.
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What is the linear parent function?
What is the linear parent function?
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Study Notes
Linear Functions
- A linear function is expressible in the form ( y = mx + b ), where ( x ) is the independent variable.
- In this equation, ( m ) represents the slope and ( b ) is the y-intercept.
- The graph of a linear function forms a straight line.
Domain
- The domain of a function is the complete set of possible input values (represented as ( x )).
- It defines the values that can be substituted into the function’s formula.
Range
- The range refers to the complete set of possible output values (represented as ( y )).
- It indicates the values produced by the function as outputs when the domain values are input.
Vertical Line Test
- This is a method used to visually evaluate if a graph represents a function.
- If a vertical line intersects the graph at more than one point, the graph does not represent a function.
Linear Parent Function
- The linear parent function is the foundational function for all linear functions, expressed as ( y = x ) or ( f(x) = x ).
- All linear functions derive their characteristics from this basic form.
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