A duty is a relation whereby a ascendancy is identified to assign specifically one worth to each facet of a domain of values. This set of resulting worths is called the variety of the function.

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Note the all attributes are relations, however not all relations are functions.


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Unless otherwise stated, the domain, or set of "input" worths is stood for by the change "x", while the set of "output" worths is represented by the change "y".

The domain variable (x) is described as the independent variable.

The variety variable (y) is described as the dependent variable.

Usually duty notation is provided to stand for a relation which is a function. Offered that relation "f" is a function, it have the right to be represented as y = f(x) (stated together "y amounts to f in ~ x"). A worth substituted into the duty is dubbed the dispute of the function.

Unless otherwise stated, independent and dependent variable are real numbers.


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One analogy offered to explain a duty is a "machine" the converts an intake value right into an output value.


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Example One

Problem

1. Explain why f: 6x - 2y = 8 is a function, and write it using role notation.

2. Advice the function for the disagreements -5, Q, 2x + 1 .

3. Graph y = f(x) and use the vertical heat test to verify it is a function.

4. State the domain and variety of the role f.

Click below for a solution.


Example Two

Problem

1. Describe why g: x2 - 2x - y - 3 = 0 is a function, and also write that using function notation.

2. Advice the role for the arguments 4, t, 2x + 1 .

3. Graph y = g(x) and also use the vertical heat test come verify that is a function.

4. State the domain and selection of the duty f.

Click here for a solution.


Example Three

Problem

1. Explain why S: x = y2 is a no function.

2. Graph relationship S and use the vertical heat test come verify the is not a function.

3. State the domain and variety of relation S.

Click here for a solution.


Example Four

Problem

1. Explain why R: x = 2y + sin(y) is a not function.

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2. Graph relationship R and use the vertical line test to verify it is not a function.