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Functions

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by

Sidney K.

on 4 September 2013

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Transcript of Functions

Functions
Function Notation
Functional Notation replaces the y in a linear notation with f(x) or f of x as a way to name a function



Equation:
f(x) = mx + b




How to Evaluate a Function
Wow! Aren't functions great?!?!
Function Form of an Equation
Domain & Range
Domain is the input

Range is the output

In other words, x and y
Re-arranging an equation into Function Notation:
Original equation:
4x + 3y = 12
-4x

-4x
3y = -4x + 12
/3

/3 /3
y = -4/3x + 4
f(x) = -4/3x + 4
How to tell if it is a function with a graph, table, or equation
With a graph you can tell if it is a function by doing the vertical line test
This is not a function because it does not pass the vertical line test
(If there is more than one point on the same vertical line it is not a function)
There are a couple ways to tell if a table is a function or not
You could graph the points and do the vertical line test
or
look at your x coordinates
x
y
Since there is more than one of the same points in the x column it is not a function. -4 and 4 cannot both go in the y column
each value of x can have no more than one value of y
Equation
(not really)
Examples
Is the table a function?
answer: yes
Is the graph a function?
Examples 2
it passes the vertical line test
Is this graph a function?
answer: no
Is the table a function?
answer: yes
There is not more than one y for one x
Coordinates (-1,0) , (-1,-1) do not pass the vertical line test
answer: no
The x point -2 has more than one y value (1.5 and -3.5)
Is the equation linear? Evaluate the function for the given value of x.
answer: yes; -7
Is the equation linear? Evaluate the function for the given value of x.
answer: no; -25
f(x) = x - 11; f(4)
Decide whether a function is linear. Then evaluate the function when x = -2
f(
x
) = -
x
² - 3
x
+5
f(
-2
) = -(
-2
)² - 3(
-2
) + 5
= 7
f(x) is not linear function because it has an x²-term
g(x) is a linear function because it has the form g(x) = mx + b
Write the function
Substitute -2 for x
Simplify
Write the function
Substitute -2 for x
Simplify
g(
x
) = 2
x
+ 6
g(
-2
) = 2(
-2
) + 6
= 2
How to tell if a funtion is linear or not
The equation does not have an x term which makes it linear
The equation does have an x term which makes it not linear
f(x) = -2/3x² - x + 5; f(6)
Full transcript