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Calculus
and Analytical
Geometry
MTH101
LECTUER
8
Graphs of
Functions
In
this section we shall
discuss-
Definition:
The
graph in the xy-plane
of a function
f
is
defined to be the graph of
the equation
y=f(x)
Example:
1
On
combining these two graphs,
we get
On
the xy-axis
Example:
4
Sketch
the graph of
Example:
2
Hence
this function can be written
as
The
graph coincides with the
line
for
x> 0 and with line
y=-x
y=x
for
x<0
.
Mth101
Page
21
Calculus
and Analytical
Geometry
Graphs
of Functions
Graph
of h(x)= x2 -
4
Or
x-2
Example:
7 Sketch
the
Example:
4 Sketch
the graph of
Example:
8
X<2
Graph
of
g(x)
= { 1
X+2
X>2
In
this form we see that
the graph can be
obtained
by translating the graph y =
x2
right
2 units because of the x-2,
and up 1 units
because
of the +1.
Mth101
Page
22
Calculus
and Analytical
Geometry
Graphs
of Functions
Here
is the graph of
Reflections
Example:
9
The
graph can be obtained by a
reflection
and
a translation:
The
curve is not the graph of
y=f(x)
for any
function
f
Mth101
Page
23
Table of Contents:
- Coordinates, Graphs and Lines
- Absolute Values
- Coordinate Planes and Graphs
- Line and Definition of Slope
- Distance, Circles, Quadratic Equations
- Functions and Limits
- Operations on Functions
- Graphs of Functions
- Limits (Intuitive Introduction)
- Limits and Computational Approach
- Limits: A Rigorous Approach
- Continuity
- Limit and Continuity of Trigonometric Functions
- Tangent Lines and Rates of Change
- The Derivative