the graph shows the function $f(x)=(2.5)^x$ was horizontally translated left by a value of $h$ to get the…

the graph shows the function $f(x)=(2.5)^x$ was horizontally translated left by a value of $h$ to get the function $g(x)=(2.5)^{x - h}$. what is the value of $h$? -2 0 2 5

the graph shows the function $f(x)=(2.5)^x$ was horizontally translated left by a value of $h$ to get the function $g(x)=(2.5)^{x - h}$. what is the value of $h$? -2 0 2 5

Answer

Explanation:

Step1: Recall horizontal translation rule

For a function (y = a^{x - h}), if (h>0), the graph of (y = a^{x}) is translated (h) units to the right; if (h < 0), the graph of (y=a^{x}) is translated (|h|) units to the left.

Step2: Use a point - by - point comparison

The original function (f(x)=(2.5)^{x}) passes through the point ((0,1)) (since (f(0)=(2.5)^{0}=1)). The translated function (g(x)=(2.5)^{x - h}) passes through the point ((- 2,1)). Substitute (x=-2) and (g(-2) = 1) into (g(x)=(2.5)^{x - h}): [1=(2.5)^{-2 - h}] Since (a^{0}=1) for (a>0,a\neq1), we have (-2 - h=0).

Step3: Solve for (h)

[h=-2]

Answer:

(-2)