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The last image is the graph of
In fact, it is an increasing exponential function, and it passes through the points , which reflects the fact that
and
, which reflects the fact that
.
Now, is a child of the parent function we just described. Precisely, it is the result of the transformation
In general, every time you perform a transformation like , you translate the graph horizontall, k units to the left if k is positive, and k units to the right if k in negative.
Since in this case , we have a horizontal translation of 4 units to the right.
So, the correct option is the third one, because:
- The first graph is the parent function translated 4 units to the left
- The second graph is the parent function translated 4 units down
- The third graph is the parent function translated 4 units to the right
- The fourth graph is the parent function