Answer:
h must be equal to - 2.
Step-by-step explanation:
See the attached graph.
The original function [tex]f(x) = (2.5)^{x}[/tex] ........... (1) is plotted in the graph denoted by the blue curve.
And the translated curve to the original function i.e. [tex]f(x) = (2.5)^{x - h}[/tex] ............ (2) is plotted in the graph denoted by the red curve.
Now, the blue curve passes through the point (0,1) point and the red curve passes through the point (-2,1) point.
Therefore, the x-coordinate gets reduced by 2 units in the translated curve corresponding to a certain y-coordinate.
Therefore, h must be equal to - 2. (Answer)
