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Questions and Answers
What is the difference between the input and the output of a function?
What is the difference between the input and the output of a function?
The input is the independent variable. The output is the dependent variable because it depends upon the value of the input.
Why does the vertical line test tell us whether the graph of a relation represents a function?
Why does the vertical line test tell us whether the graph of a relation represents a function?
When a vertical line intersects the graph of a relation more than once, that indicates that for that input there is more than one output.
How can you determine if a relation is a one-to-one function?
How can you determine if a relation is a one-to-one function?
First check to see if the relation is a function. Then check to see if each output corresponds to one unique input.
What type of representation is described? A large drum stores sugar used to mass produce ice cream. The drum holds 75 gallons of sugar and dispenses 0.18 gallons of sugar to make each carton of ice cream.
What type of representation is described? A large drum stores sugar used to mass produce ice cream. The drum holds 75 gallons of sugar and dispenses 0.18 gallons of sugar to make each carton of ice cream.
What is the equation form for a linear function?
What is the equation form for a linear function?
What is the equation notation for a function?
What is the equation notation for a function?
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Study Notes
Functions and Their Characteristics
- The input of a function represents the independent variable, while the output represents the dependent variable, reliant on the input value.
- A function can be visually assessed using the vertical line test: if a vertical line crosses a graph at more than one point, it indicates multiple outputs for a single input, thus the relation is not a function.
- To ascertain if a relation is a one-to-one function, confirm it is a function first (each input has one output). Subsequently, verify that each output is linked to a unique input, indicating it is one-to-one.
Types of Mathematical Representation
- Word form provides descriptive accounts of relationships; for example, a drum holding 75 gallons of sugar dispenses 0.18 gallons per ice cream carton, demonstrating a functional relationship between sugar quantity and production volume.
- Equation form is succinctly expressed as y = mx + b, where m represents the slope and b the y-intercept.
- Equation notation formalizes the function in the format f(x) = mx + b, indicating it operates on inputs for specific outputs.
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