Obj. 7.4: Parent functions and transformations
Guided Notes
While you do have a GDC, it is important to be familiar with the following “parent functions” and
key elements of them. For each parent function listed below, please use the video to help:
a) Record the function
b) Sketch the graph
c) Identify (label/describe) the following key elements:
-
vertex/focal point
- domain
-
any symmetries
- any asymptote(s)
range
- any key value(s)
max/min
NOTE: A vertical asymptote models a limit to the domain, while a horizontal asymptote models
a limit to the range. Graphically, these are modeled with dashed lines. The line contains the input
or output value(s) for which the graph is undefined.
Linear
Quadratic
Exponential (growth)
Absolute Value
Cubic
Inverse (1/x-1)
Square Root
1/x2
Starting at 6:34 in the video, we see a description of general transformations. Please use the video
to fill in the table below.
If we have a starting parent function y = f ( x ) , then the transformations that we need to consider
can be represented as y = a × f ( x - h) + k , where the variables represent the following:
Variable
Type of Transformation
Mapping
a
(x, y) 
h
(x, y) 
k
(x, y) 
Now, complete the following examples. Please pause the video as you work, then play to check.
Parent
Transformation
y = x2
y = ( x + 3) - 2
(x, y) 
y= x
y = -2 x -1
(x, y) 
y=
1
x
y= x
2
Mapping
3
x +1
(x, y) 
1
x +3
2
(x, y) 
y=
y=
Words