How does #y=5^(x+1) - 2# relates to its parent function?

1 Answer
Apr 23, 2017

Answer:

The transformed function is horizontally translated #1# unit to the left and vertically translated #2# units down.

Explanation:

So the parent function is #y=5^x#. Look like this:

graph{5^x [-10, 10, -5, 5]}

With the transformed function of #y=5^(x+1) - 2#, there are 2 changes done.

  1. The #d#-value. Tells us how far the function translate from the left to right, however, you have to isolate the value from the exponent. In this case, the function is translated #1# unit to the left.
  2. The #k#-value. Tells us the vertical translations of the function. In this case, the function is translated #2# units down.

As a result, the function looks like this:

graph{5^(x+1) - 2 [-10, 10, -5, 5]}

Note that the #5# is NOT the #a#-value - it is the base value.

Hope this helps :)