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Parent, Piecewise, and Transformed Functions
Contributed by: Villalobos
● Parent Functions

◌ Piecewise Functions

◌ Transforming functions


Click then drag the equation by the description.
Absolute value function
Constant function
Cubic function
Cube root function
Exponential function
Greatest Integer function
Identity function
log base b function
Quadratic function
Reciprocal function
Square root function
y=logb(x)
?
y=[x] or y=int(x,1)
?
y=|x|
?
y=x3
?
y=∛x
?
y=bx
?
y=1
?
y=√x
?
y=1/x
?
y=x2
?
y=x
?
f(x)
x
-2
0
2
Equation:
Domain: xε
Range: f(x) ε
Parent Function
f(x) =
 (-∞,∞)
?
 {1}
?
f(x)
x
-1
0
1
Equation:
Domain: xε
Range:
a.k.a.
Identity function
?
Parent Function
f(x) =
{f(x) εℛ }
?
(-∞,∞)
?
f(x)
x
-2
-1
0
1
2
Equation:
Domain: xε
Range: f(x) ε
a.k.a.
Square function
?
parent function
f(x) =
(-∞,∞)
?
[0,∞)
?
f(x)
x
-1
-1
?
-⅛
?
-½
0
0
?
⅛
?
½
1
1
?
8
?
2
Equation:
Domain:
Range:
parent function
f(x) =
f(x) ε (-∞,∞)
?
x ε (-∞,∞)
?
f(x)
x
-4
4
?
-2
2
?
0
0
?
1
?
1
3
3
?
5
?
5
parent function
Equation:
Domain: xε
Range: f(x) ε
f(x) =
{
f(x) =
-x,
x,
(-∞,∞)
?
[0,∞)
?
x<0
?
x≥0
?
f(x)
x
-2.5
-3
?
-1
-1
?
0
?
0
1.8
1
?
3
?
3
Eq:
parent function
Domain: xε
Range:
f(x) ε
 Rounds up
Rounds down
a.k.a.
Greatest Integer
 Function
?
f(x) =
{...,-2,-1,0,1,2,...}
?
int(x,1)
?
(-∞,∞)
?
Open excel and look up the Ceiling function and
 enter its description below:
Open excel and look up the FLOOR function and
 enter its description below:
The greatest integer function returns the greatest
integer less than or equal to the argument.
The smallest  integer function returns the smallest
integer greater than the argument.
f(x)
x
0
1
4
9
Domain: xε
Range: 
Equation:
a.k.a. f(x)=

The inverse of x2 .
f(x) ε [0,∞)
?
f(x) =
[0,∞)
?
SQRT(X)
?
parent function
√x
?
f(x)
x
-1
-1
?
-½
-⅛
?
0
?
0
⅛
?
½
1
?
1
8
?
2
Equation:
Domain: xε
Range: 
parent function
a.k.a. f(x)=

The inverse of x3.
f(x) =
f(x) ε (-∞,∞)
?
(-∞,∞)
?
x1/3
?
∛x
?
Copy the key press sequence to graph
 f(x)=∛x.
f(x)
x
-⅓
?
-3
-½
?
-2
-1
?
-1
d.n.e.
?
0
1
?
1
½
?
2
⅓
?
3
Equation:
Domain:
Range: 

a.k.a. f(x) =
The inverse of x.
d.n.e = 
parent function
does not exist.
?
{xε ℛ, x≠1}
?
f(x) =
{y∊ℛ, y≠0}
?
x-1
?
1/x
?
◌ Parent Functions

● Piecewise Functions

◌ Transforming functions


Enter these equations
to graph the peicewise
function of 4 peices.
Press GRAPH.
Type code
given to you
by your
teacher.
The cieling function rounds up to
the nearest integer away from zero.
?
CIELING(x,1) =↱x↰
The floor function rounds down to
the nearest integer toward zero.
?
f(x) = int(x) =
FLOOR(x,1) =↳x↲
{
ceiling(x)=↱x↰
?
floor(x) =↳x↲
?
x≥0
x<0
◌ Parent Functions

◌ Piecewise Functions

● Transforming functions



Write the transformations made to f(x) to obtain g(x).
translation, shift, to the right by      units.
reflection over the x-axis indicated by
translation, shift, up by        units.
vertical dilation by a factor of
6
?
2
?
7
?
" - "
?
Write the transformations made to f(x) to obtain g(x).
translation to the left by      units.
reflection over the x-axis indicated by
translation down by        units.
vertical dilation by a factor of
9
?
7
?
2
?
" - "
?
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