Question

What is the value of h?

The graph shows the function f(x) = (2.5) was horizontally
translated left by a value of h to get the function g(x) = (2.5)
-2.
0
2
5

Answer 1

A -2

Explanation:

Answer 2

Option (1). h = -2

Explanation:

This question is incomplete: here is the complete question.

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

`(2.5)^(x+2)` =
`(2.5)^(x-h)`

By comparing both the sides,

x + 2 = x - h

h = -2

Therefore, Option (1) will be the answer.