section 2.5 transformation of functions. graphs of common functions
TRANSCRIPT
x
y
Reciprocal Function
Domain: - ,0 0,
Range: - ,0 0,
Decreasing on - ,0 0,
Odd function
and
1( )f x
x
Vertical Shifts
Let be a function and be a positive real number.
The graph of is the graph of shifted units
vertically upward.
The graph of is the graph of shifted
f c
y f x c y f x c
y f x c y f x c
units
vertically downward.
Horizontal Shifts
Let be a function and a positive real number.
The graph of is the graph of shifted
to the left units.
The graph of is the graph of shifted
to the
f c
y f x c y f x
c
y f x c y f x
right units.c
Vertically Stretching
x
y
x
yGraph of f(x)=x3
Graph of g(x)=3x3
This is vertical stretching – each y coordinate is multiplied by 3 to stretch the graph.
A function involving more than one transformation can be graphed by performing transformations in the following order:
1. Horizontal shifting
2. Stretching or shrinking
3. Reflecting
4. Vertical shifting
A Sequence of Transformations
Move the graph to the left 3 units
Starting graph.
Stretch the graph vertically by 2.
Shift down 1 unit.
(a)
(b)
(c)
(d)
x
y
Use the graph of f(x)= x to graph g(x)= -x.
The graph of g(x) will appear in which quadrant?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
( )f x x
(a)
(b)
(c)
(d)
x
y
Write the equation of the given graph g(x). The original function was f(x) =x2
g(x)
2
2
2
2
( ) ( 4) 3
( ) ( 4) 3
( ) ( 4) 3
( ) ( 4) 3
g x x
g x x
g x x
g x x