Answer:
Option (1). h = -2
Step-by-step explanation:
This question is incomplete: here is the complete question.
The graph shows the function f(x) = [tex](2.5)^{x}[/tex] was horizontally shifted by a value of h to get the function g(x) = [tex](2.5)^{x-h}[/tex]. What is the value of h ?
From the graph attached,
Point (0, 1) lies on function f(x).
If the graph of function f(x) is shifted h units left horizontally, rule for the translation will be,
f(x + h) → g(x)
For 2 units shift to the left horizontally,
f(x + 2) → g(x)
[tex](2.5)^{x+2}[/tex] = [tex](2.5)^{x-h}[/tex]
By comparing both the sides,
x + 2 = x - h
h = -2
Therefore, Option (1) will be the answer.
