Shelby Sell
Sammie Meddaugh
Emily Wojahn
 Transformation:
Functions that map
real number to real numbers.
 Rigid
Transformations: Leave the
side and shape of the graph
unchanged (horizontal and vertical
translations, reflections).
 Non
Rigid Transformations: Distort
the shape of a graph (horizontal or
vertical stretches and shapes).
 If
c is a positive real number:
Horizontal
y= f(x-c)
A translation to the right by c
y= f(x+c)
A translation to the right by c
units
units
Vertical
y= f(x) + c
A translation up by c units
y= f(x) - c A translation down by c units
y= abs(x)
y= abs(x – 2)
2
y= x2
y= x2 + 3
Across the x-axis
y= -f(x)
(x,y)
Across the y-axis
y= f(-x)
(x,y)
Through the origin
y= -f(-x)
(x,y)
(x,-y)
(-x,y)
(-x.-y)
Reflection
over y= x
axis
Reflection
over y axis
Reflection over x axis
Horizontal Stretch/Shrink
A stretch by a factor of c if c>1
y= f (x/c)
A shrink by a factor of c if c<1
Vertical Stretch/Shrink
y= c f(x)
A stretch by a factor of c if c> 1
A shrink by a factor of c if c<1
Graph y = 3x²
y = x²
Graph of y = x²
Multiply all red
values by 3 to get
coordinates for
the new graph.
"Transformations on the
Basic Parabola." W.A.E.C.E.
Math Help. N.p., n.d. Web.
Graph of y = x²
with a stretch of 3.
Given y=x²
 1.)
Horizontal shift 2 units to the right y=(x-2) ²
 2.) Stretch Vertically by factor 3 y=3(x-2) ²
 3.) Vertical Translation 5 units up y=3(x-2) ² +5
Y= f(x) Entire functions
absolute value

(change negative y values to
positive)
Y= - f(x) Only Negative y
values
2
A) y = ½x2 + 2
C) y = 3(x + 2)2
B) y = 3x2 + 2
D) y = ½(x + 2)2
3
A) y = ½(x -
3)2
C) y = 2(x - 3)2
2
B) y = ½(x + 3)2 D) y = 2(x + 3)
A y = 0.5(x +
1)4
B y = 0.5(x - 1)4
C y = 2(x + 1)4
D y = 2(x - 1)4
Describe how the graph of y= x²
can be transformed to the graph
of the given equation
Y=x²-3
A) Vertical translation up 3 units
B) Horizontal translation to the right 3 units
C) Horizontal translation to the left 3 units
D) Vertical translation down 3 units
 Given
function f, which of the following
represents a vertical stretch by a factor of
3.
A) y=f(3x)
B) y=3f(x)
C) y=f(9x/3)
D)y=f(x)/3
 Given
a function f, which of the following
represents a vertical translation of 2 units
upward, followed by a reflection across the
y-axis.
 A)
y=f(-x) + 2
C) y= -f(x-2)
 B)
y= 2-f(x)
D) f(x) -2
TRUE
The
OR FALSE?
function y=f(x+3) represents
a translation to the right by 3
units of the graph of y = f(x).
TRUE
The
OR FALSE?
function of y=f(x)-4
represents a translation down 4
units of the graph of y=f(x)
 Write
an equation whose graph is
 Y=x
²; a vertical stretch by a factor of 3,
then shift right 4 units
 A)
y=3(x-4) ²
C) y=3x ² -4
 B)
y=-3x ² +4
D) y=3(x+4) ²
 Write
an equation whose graph is
 Y= x ; a shift left 2 units, then a vertical
stretch y a factor of 2, and finally a shift
down 4 units.
 A)
2 x+2 -4
C) 2 x-2 +4
 B)
2(x+2) -4
D) 3(x-2) +4
 1.)
B
 2.) A
 3.) A
 4.) D
 5.) B
6.) A
7.) False, it is
translated left.
8.)True
9.) A
10.)A
http://www.mathopolis.com/questions/q.php?id=555&site=1&ref=/sets/functiontransformations.html&qs=555_556_557_558_1191_2440_1192_2441_2442
http://departments.jordandistrict.org/curriculum/mathematics/secondary/impact/
Algebra%20II/Ready%20for%20web%20site/zTransformationMatchingGame.pdf
http://tutorial.math.lamar.edu/Classes/Alg/Transformations.aspx
Pre calculus- Eighth edition book
http://cheezburger.com/6321270784
"Transformations on the Basic Parabola." W.A.E.C.E. Math Help. N.p., n.d. Web.