How do you use the graph of #f(x)=10^x# to describe the transformation of #g(x)=10^(-x+3)#?

1 Answer
Alex P.
Apr 25, 2017

#g(x) = f(-(x-3))#

A translation by 3 in the x direction followed by a reflection.

Explanation:

I hate these combined transformation type questions. What you need to look at here is the argument for the function.

#f(x)=10^x#

#g(x)=10^(-x+3)#

so it follows that

#g(x)=f(-x+3)#

We should know that #f(-x)# is a reflection of #f(x)# and #f(x - a)# is a translation of #f(x)# by #a# in the x direction (sorry, can't seem to write vectors on here). The difficult thing to get your head around is the order in which the transformations are applied.

By writing #-x+3# as #-(x-3)# it should help you to realise the shift.
graph{10^(-x+3) [-1.077, 6.523, -0.44, 3.36]}

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