Question

Could someone help me with this?

The red graph (1) is the graph of f(x) = 2x. Describe the transformation of the blue function (2) and write the equation of the graph.

Answer 1

Well we can see that the red graph being 2^x seems to begin from x = 0....(even though it never really does reach 0

Regardless...to move that up 2 units so that the same graph would seem to start at x = 2....we would need a vertical shift up 2 right?

so right away we have the blue line will be something like

y = 2^x + 2

Answer 2

But..we are not done....before (red) it looks like it goes through the y-axis at 1 and it goes through at a certain point...but now (blue) it goes through at a different point (seems like the blue graph is a bit more to the right)

Answer 3

In order to shift something horizontally to the right...we need to subtract a value from the 'x'...

so we have

\[\large y = 2^{x - ?} + 2\]

what would be the '?'