Find angle E, F, and side e

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