If the point (0,0) is on the graph of y=f(x), which of the following points must be on the graph of y=f(x-2)+3? a)(2, -3) b)(2,2) c)(2,3) d)(-2,-3) e)(-2,3)

1 Answer
Mar 18, 2018

C

Explanation:

So let's do this two ways: using transformations of a function, and using the logic behind those transformations.

Transformations
We know that the transformation #x rightarrow x-2# shifts all points 2 to the right while transforming #y rightarrow y+3# shifts everything up three, hence (0,0) becomes (2, 3) i.e. c.

Logic
The only thing we know about the function #f(x)# is that #f(0) = 0#.
Well, if we want to mess with the given equation for y
#y = f(x-2) + 3 #
so that the argument of #f# is 0, we obviously need #x-2=0# or #x = 2#.
When we plug in the value for #f(0)# i.e. 0, we see that #y = 0 + 3 = 3#, as shown before.