Question

Which function represents the graph of h(x)=2|x−3|+1 after it is translated 2 units to the right?

A.f(x)=2|x−3|+3

B.f(x)=2|x−3|−1

C.f(x)=2|x−5|+1

D.f(x)=2|x−1|+1

Answer 1

Your answer is C.f(x)=2|x−5|+1.

Given graph: h(x)=2|x−3|+1

When you have to translate a graph towards right by some unit m, replace all x in the graph with (x-m).

So after translating it by 2 units towards right, h(x) will becomes g(x) where

g(x) = h(x-2) = 2|x-2 - 3| +1 = 2|x-5| + 1

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Rules for graph transformation:

1. When you have to move the graph y = f(x) towards RIGHT by m units, the new graph becomes y = f(x-m)

2. When you have to move the graph y = f(x) towards LEFT by m units, the new graph becomes y = f(x+m)

3. When you have to move the graph y = f(x) UP by m units, the new graph becomes y = f(x) + m

4. When you have to move the graph y = f(x) DOWN by m units, the new graph becomes y = f(x) - m