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

Apr 23, 2017

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 :)