Reflection Of Graphs Of Functions

The reflections of graphs in the x and y axes are explored by comparing the graphs of f(x), -f(x), f(-x) and - f(-x): f(x) ( blue ) , - f(x) ( green ), f(- x) ( red ) and - f( - x) ( magenta ).

The function f(x) is a quadratic function of the form

f(x) = ax 2 + bx + c

The exploration is carried out by changing the parameters a, b and c included in f(x) above. Follow the tutorial below.

<

a =
-10+10

b =
-10+10

c =
-10+10

>

TUTORIAL 1 - click on the button above "draw" to start.

2 - The four graphs displayed are those of functions
f(x) ( blue ) , - f(x) ( green ), f(- x) ( red ) and - f( - x) ( magenta ). Do the following for different values of parameters a, b and c:

A - Use the tutorial on
reflections of graphs in x-axis to explain the relationship between the graphs of f(x) and that of -f(x).

B ) Use the tutorial on
reflections of graphs in y-axis to explain the relationship between the graphs of f(x) and that of f(-x).

3 - Use what you have learned above to explain the relationship between:

A ) f(-x) and -f(-x).

B ) f(x) and -f(-x).

C ) -f(-x) and -f(x).

More on reflections:

Reflection Of Graphs In x-axis.

Reflection Of Graphs Of Functions.