Download Function Notation and Parent Functions

Function Notation and
Parent Functions
Objective: Students will be able to write equation in function notation
and interpret how to evaluate them. Students will be able to identify
the 5 main parent functions.
Function Notation
Writing an equation without using the y vale
f(x) instead of y
This is read as f of x, this notation does not mean multiplication
They really mean the same thing, but it is a better way to show a
relationship between numbers
h(t) for example could be a problem the has the height (h) of an object
in terms of the time (t) it is in the air, the individual variables tell you
something
It also allows you to write multiple equations without them all equal to
y
Evaluating a Function
f(x)=2x+3
f(3)=2(3)+3
f(3)=9
Independent value is 3
Dependent value is 9
(3,9)
The difference is that they tell us what to sub in for x right in the
function instead of stating solve the equation when x=3
Parent Functions
5 Main functions we will discuss in this class and can be the basis for
other classes to follow
You should know the name, basic function and graph
1. Linear
2. Quadratic
3. Cubic
4. Square Root
5. Absolute value
Linear
y  mx  b
What would be
Domain and Range?
All real numbers for
D and R since lines
never end
How would this
look in a table?
Adding the same
value to the
dependent variable
as independent
increases by 1
Quadratic
Chart Title
10
9
8
7
yx
6
2
5
4
3
2
Graph is called a parabola
1
0
-4
What is D and R
What it might look
like in a table?
D all real numbers
R could have a low or
high point and then go
on forever in one
direction
The second pattern
is constant
-3
-2
-1
0
-3
-2
-1
0
1
2
3
1
9
4
1
0
1
4
9
2
3
4
Cubic
Chart Title
30
20
yx
3
10
0
-4
-3
-2
-1
0
-10
What is D and R
What it might look
like in a table?
D All Real numbers
R All Real numbers
Third pattern would
have a constant
number
-20
-30
-3
-2
-1
0
1
2
3
-27
-8
-1
0
1
8
27
1
2
3
4
Square Root
Chart Title
y x
4.5
4
3.5
Has a definite
starting point
D and R go on for
ever from the
starting point
What is D and R
3
2.5
2
1.5
1
0.5
0
0
0
1
4
9
16
0
1
2
3
4
2
4
6
8
10
12
14
16
18
Absolute Value
Chart Title
y x
3.5
3
2.5
2
What is D and R
What it might look
like in a table?
Very similar to quadratic,
sides are linear not
curved
D all Real numbers
R from vertex on
All positive answers
1.5
1
0.5
0
-4
-3
-2
-1
0
-3
-2
-1
0
1
2
3
1
3
2
1
0
1
2
3
2
3
4
Homework
Pg 414
1 do not switch to y1 and y2, keep as function notation and state
answer
2, 6