Functions
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Functions. f(x)=2x-7. g(x)=x+12. Definitions. A function is a special kind of relation that can be described by a formula. (A relation is set of ordered pairs; some relations have a pattern and can be described by a formula.). Functions.

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Functions
Functions

f(x)=2x-7

g(x)=x+12


Definitions
Definitions

  • A function is a special kind of relation that can be described by a formula.

  • (A relation is set of ordered pairs; some relations have a pattern and can be described by a formula.)


Functions1
Functions

  • A function is a special kind of relation. Not all relations can be called functions!

  • Functions are the relations that mathematicians study most.

What makes a relation a function?

Good question!


In a function
In a function,

each input value can give only one output value.

Does that make sense?

Think about it: If you put a number into a function, you want to know that only one number can come out.


Consider this relation
Consider this relation:

If you put a number in, is there only one possible number that could come out?


For any input value, there is only one possible output value.

Is there any number you can subtract 11 from and have more than one possible answer (output)? Click to see...

So this is a function.


One way to write this function would be
One way to write this function would be, value.

  • When we write it like this,

    x is the input value,

    and y is the output value.


Evaluate functions
Evaluate Functions value.

  • Evaluating a Function is substituting a value for x & calculating y.

  • Evaluate this function if x = 42: substitute 42 for x, and calculate y.


The value. domain of a function is the set of all input, or x-values.

The domain may be restricted to a list of numbers, or it may open to all numbers. This information is provided with the function.

The range of a function is the set of all possible output, or y-values.

The range can be determined from the domain and formula.


So in our last example, if 42 belongs to the value. domain of the function,

then 31 belongs to the range.


Another way to write a function is to use value. function notation.

Function notation looks like this:

Read that, “F of x equals two x plus 1.”


Given value.

Writing the function this way shows us that x is clearly the input variable.

When asked to evaluate a function it will look like this:

find f (-2).


Given value.

Again, we substitute the value for x and calculate y.

find f(-2).

Replace every x with –2.


Given: value.

If you replace every x with –2,

evaluate:


Evaluate These Function Values value.

Given:

Find:


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