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What transformation occurred from the parent function, y=(1)/(x)? y=(1)/(x-3)

User Roborourke
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In order to understand transformations of functions, first we need to have an innate understanding of what a parent function is.

A parent function is the simplest function of a family of functions. For this problem, we are working with the family of functions where y=1/x is the parent function.

Now, when we say transformation, these are changes that occur to the parent function to form a new one. There are four main types of transformations: shifts (both horizontally and vertically), reflections, and stretches/compressions.

For this problem, we can see that the changes occur inside the parentheses. We've changed from y=1/x to y=1/(x-3). Everything else has remained the same except for that subtraction of 3 in the denominator of the fraction.

Now, transformations that occur inside the parentheses--that is, that apply directly to the x-values--are horizontal transformations. If it was outside of the parentheses, we'd call it a vertical transformation.

Our x in the function has been replaced with (x-3). This indicates a horizontal shift.

When we see x-c (where c is a positive number), we are looking at a horizontal shift to the right by c units, because the minus sign tells us where the function moves. For the new function y=1/(x-3), the parent graph y=1/x has shifted to the right by 3 units.

So, the transformation that occurred from the parent function y=1/x to y=1/(x-3) is a horizontal shift of 3 units to the right.

User Louis Barranqueiro
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