Transcript Notes 1

Functions
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
• 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,
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:
x  11
If you put a number in, is there only one
possible number that could come out?
any
value,
is only11
IsFor
there
anyinput
number
you there
can subtract
fromone
andpossible
have moreoutput
than one
possible
value.
answer
Click to see...
So (output)?
this is a function.
23  5 99
x  11
12  16 88
One way to write this function would be,
y  x  11
• When we write it like this,
x is the input value,
and y is the output value.
Evaluate Functions
• Evaluating a Function is substituting a value
for x & calculating y.
• Evaluate this function if x = 42: substitute
42 for x, and calculate y.
y  42
31
x 11
11
The 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
domain of the function,
y  x  11
When x  42,
y  31
then 31 belongs to the range.
Another way to write a function is
to use function notation.
Function notation looks like this:
f  x  2x  1
Read that, “F of x equals
two x plus 1.”
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:
Given f  x   2 x  1,
find f (-2).
Again, we substitute the value for x
and calculate y.
Given f  x   2 x  1,
find f(-2).
Replace every x with –2.
If you replace every x with –2,
evaluate:
Given:
f x2  2(x
11)1
2342
Evaluate These Function Values
Given:
Find:

f x  5x  9
f   8  49
f 0  9
f 7   26