Question

How does the graph of y = 2 x - 1 compare to the graph of y = 2 x ? y = 2x - 1 is translated left 1 unit. y = 2x - 1 is translated down 1 unit. y = 2x - 1 is translated right 1 unit. y = 2x - 1 is translated up 1 unit.

Answer 1

y = 2^(x - 1) is translated left 1 unit.

Answer 2

The difference between the two given equations is that 1 is subtracted from 2x in the first equation while this is missing from the second. If we are going to add 1 to both sides of the first equation, we get the answer of,

y + 1 = 2x - 1 + 1
y + 1 = 2x

As we can see, the equation above is similar to y = 2x except that +1 is added to the y value. Thus, your graph is translated 1 unit up.