Transcript Functions 4-6

Functions 4-6
I can determine whether a relation is a function and find function
values.
S. Calahan
2008
What is a function?
• A function is a relation in which
each element of the domain is
paired with exactly one element
of the range.
Identify Functions
x
y
-4
-1
1
3
9
-6
11
This is a function since each element
of the domain (x) corresponds to only one
element in the range (y).
It doesn’t matter if two elements of the domain are paired with
the same element in the range.
Identify Functions
x
y
-3
6
2
5
3
1
2
4
The table represents a relation that is not
a function because there are two of the
same elements in the domain (x).
Vertical Line Test
• Use the vertical line test to determine if a
graph represents a function.
• If a vertical line can be drawn so that it
intersects the graph no more than once
the graph is a function.
• If a vertical line can be drawn so that it
intersects the graph at two or more
points the graph is not a function.
Vertical Line Test
• Not a function, because it crosses twice
Vertical line test
• This is a function because it crosses only
once no matter where you draw the line.
Function Notation
• Equations that are functions
can be written in function
notation form
• Example: y = 3x – 8 equation
f(x) = 3x – 8 function notation
Function Values
• f(x) = 2x + 5 for f(-2)
f(-2) = 2(-2) + 5
=1
Substitute the value inside the ( )
in for the variable inside the ( ).
f(x) = 2x + 5
• f(1) + 4 = [2(1) + 5] + 4
Substitute the 1 in for the x then add the
4 at the end of the expression.
= [2 + 5] + 4
= 7 + 4 = 11
simplify
add
Nonlinear Functions
• A function that is nonlinear can
be solved the same way as a
linear function. Nonlinear
functions can have an exponent
on one of the variables.
2
• f(n) = n – 3n + 4
f(n) =
2
n
– 3n + 4
• f(4) = 42 – 3(4) + 4
= 16 – 12 + 4
=4+4=8