How do you identify the transformation of #h(x)=abs(x+3)-5#?

1 Answer
turksvids
Dec 9, 2017

The graph of #f(x)=|x|# is shifted 3 units to the left and 5 units down.

Explanation:

Transformations of the #g(x)=f(x-c)# are horizontal shifts of #c#-units. The negative sign in there is particularly important. I usually find the shift by setting #x-c=0# and then solving. In this case #x+3=0\rightarrow x=-3#, so the graph is shifted 3 to the left (because of the negative sign).

Transformations of the form #g(x)=f(x)+d# are vertical shifts. In this case the shift goes exactly how you'd expect, with a positive value being a shift up and a negative value being a shift down, so the #-5# means a shift of 5 units down.

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