Transcript Segments and Angles - Mr. Rosen's Class Website

Functions
Def. A function is an ordered pairing of x
and y values such that each x-value
(input) is paired with only one y-value
(output).
Do any of the vending machines represent
functions? Explain your answer.
Machine #1
Choice #
What you get
1
M&Ms
2
Pretzels
3
Dried fruit
4
Hershey’s bar
5
Fat free cookies
6
Snickers bar
Machine #2
Choice #
1
2
3
What you get
Machine #3
Choice #
What you get
M&Ms or dried
fruit
1
M&Ms
2
M&Ms
Pretzels or
Hershey’s bar
3
Pretzels
Snickers or fat
free cookies
4
Dried fruit
5
Hershey’s bar
6
Hershey’s bar
7
Fat free cookies
8
Snickers
9
Snickers
Domain: set of all x-values (inputs)
Range: set of all y-values (outputs)
Can we determine the Domain and
Range of Vending Machine #3?
Choice #
What you get
1
M&Ms
2
M&Ms
3
Pretzels
4
Dried fruit
5
Hershey’s bar
6
Hershey’s bar
7
Fat free cookies
8
Snickers
9
Snickers
4 Ways to represent a function:
1. Table
2. Words
3. Graph
4. Equation
Explain if each of the following relations
are functions. Write the domain and range
of each.
Table:
x
0
3
2
-1
3
y
5
7
-3
0
4
Words: The radius of a sphere and its volume.
Graph: Which relation below is a function?
Explain.
4
4
2
2
-5
Equation:
Rather than writing y = x2, we can use
function notation:
f (x) = x2
To find the value of the function when x = 4,
we would write f (4):
f (4) = 42 = 16
For the function machine below, we would
write f (x) = x2 + 2x + 1. The f is just the
name of the function; it is not a variable.
g(x) = x2 + 2x + 1
(x) = x2 + 2x + 1
BOB(x) = x2 + 2x + 1
 Make sure you don’t
treat f (x) as
multiplication
2
f  x   x  2x  1
Ex. If f (x) = -x2 + 3(x – 1), evaluate f (4):
Ex: If g (x) =
a) g(-1):
b) g(1 4 ):
x2
evaluate:
Ex. Use the graph to
find the values.
a) f (-4)
b) f (0)
c) All x-values where
f (x) = 3.
y
f (x)
x
A linear function can be written in the form
f (x) = mx + b
f (x) = 2x + 5
y=x–8
s(t) = 5t
g(r) = 9
The graph will be a line.