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).

A quadratic function of the form

f(x) = ax2 + bx + c

is used to explore the relationship between the graphs of f(x), -f(x), f(-x) and -f(-x).

TUTORIAL

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1 - click on the button above "click here to start" and MAXIMIZE the window obtained.

2 - The four graphs displayed are those of functions f(x), f(-x), -f(-x) and -f(x). 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).

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