Question

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

Answer 1

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 :)