The graph shows the function f (x) = (2.5) x was horizontally translated left by a value of h to get the function g (x) = (2.5) x-h.

F (x) = (2.5) ^x

g (x) = (2.5) ^ (x - h)

You should know that when you add a constant to the argument of a function the graph moves left h unit, this is the graph of f (x + h) is the graph of f (x) shifted h units leftward.

You can make this table for f (x) and g (x)

x f (x) = (2.5) ^x g (x) [from the graph]

-3 (2.5) ^ (-3) = 0.064 0.4

-2 (2.5) ^ (-2) = 0.16 1

-1 (2.5) ^ (-1) = 0.4 2.5

0 1

1 2.5

2 (2.5) ^2 = 6.25

From that table you can see that:

g (-3) = f (-1)

g (-2) = f (0)

g (-1) = f (1)

And you can infere that g (x) = f (x + 2)

Then, g (x) = (2.5) ^ (x - h) = (2.5) ^ (x + 2)

Which implies that x - h = x + 2 = > h = - 2.

Then the answer is h = - 2