# Calculus And Analytical Geometry

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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