TRANSFORMATION OF FUNCTIONS: REFLECTION
A reflection is a transformation that flips a graph over a line, called the line of reflection.
Reflection about the xaxis and yaxis
 The graph of y =  f(x) is the reflection of the graph of y=f(x) about the xaxis.
 The graph of y = f(x) is the reflection of the graph of y=f(x) about the yaxis.

Examples
Example 1
Use the graph of f(x)= x2 to obtain the graph of g(x)=  x2.
Solution :
Since g(x)=  f(x) then the graph of g(x) is the reflection of the graph of f(x) about the xaxis.
First, graph f(x)= x2 (blue graph) and then reflect (flip) it about the xaxis to obtain the graph of
g(x)=  x2 (red graph).
Example 2
Try these problems
QUESTIONS
Use the graph of f(x) = x to obtain the graph of g(x)= x.
Use the graph of f(x)=x3 to obtain the graph of g(x)=  x3.
Use the graph of f(x)=√x to obtain the graph of g(x)=  √x.
Use the graph of f(x)=√x to obtain the graph of g(x)=  √x..
ANSWERS

Use the graph of f(x) = x to obtain the graph of g(x)= x.

Use the graph of f(x)=x3 to obtain the graph of g(x)=  x3.

Use the graph of f(x)=√x to obtain the graph of g(x)=  √x.

Use the graph of f(x)=√x to obtain the graph of g(x)=  √x..

To graph g(x)= x, we first graph f(x) = x (blue graph) and then reflect it about the xaxis.
The graph of g(x)= x is the red graph.

To graph g(x)=  x3, we first graph f(x)=x3 (blue graph) and then reflect it about the xaxis.
The graph of g(x)=  x3 is the red graph.

To graph g(x)=  √x, we first graph f(x)= √x (blue graph) and then reflect it about the xaxis.
The graph of g(x)=  √x. is the red graph.
Note that the domain of both functions is x ³ 0.

Use the graph of f(x)= √x to obtain the graph of g(x)= √x.
To graph g(x)= √x, we first graph f(x)= √x (first graph) and then reflect it
about the yaxis (second graph).
Note that the domain of f(x) is x ³ 0 while that of g(x) is x £ 0.