 Analysis and Development of Mathematical Rules
Translations of Graphs The above picture was generated with mathematica using the rules of translations.

1.  Graph the functions y = x, y = x+2, y = x-2, and y = x+5 on the same plane. 2.  Compare the four graphs.  Describe the effect of adding or subtracting a constant to the function y = x.

When you add a number to the graph it moves it up.  The number that is added is the number of units it moves up.
When you subtract a number to the graph it moves it down.  The number that is subtracted is the number of units it moves down.

3.  Now graph y = x2, y = x2+2, y = x2-2, y = x2+5 on the same plane. 4.  Compare the four graphs.  Describe the effect of adding or subtracting a constant to the function y =x2.

When you add a number to the graph it moves it up.  The number that is added is the number of units it moves up.
When you subtract a number to the graph it moves it down.  The number that is subtracted is the number of units it moves down.

5.  Develop general mathematical rules to describe the above noted effects.

y = x + k    moves line k units up.
y = x - k    moves line k units down.

y = x2 + k.   moves curve k units up.
y = x2 - k.   moves curve k units down.

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