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) where:
f(x) ( blue )
- f(x) ( green )
f(- x) ( red )
- f( - x) ( magenta ).
The function \( f(x) \) is a quadratic function of the form
\[ f(x) = a x^2 + b x + c \]
The exploration is carried out by changing the parameters \( a, b \) and \( c \) included in \( f(x) \) above. Follow the tutorial below.
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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: