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4. The figures below are similar. What is the length

iamjenng9330

16.01.2020

$g(x)=(10)^{x-3}$

Step-by-step explanation:

* Lets explain how to solve the problem

- The form of the exponential function is $f(x)=a(b)^{x}$ , where

a is the initial amount (x = 0) , b is the growth factor

- If b > 1 , then the function is exponential growth function

- If 0 < b < 1 , then the function is exponential decay function

- If the function translated horizontally by h units to the right , then

the new function is $g(x)=a(b)^{x-h}$

- If the function translated horizontally by h units to the left , then

the new function is $g(x)=a(b)^{x+h}$

- If the function translated vertically by k units up , then the new

function is $g(x)=a(b)^{x}+k$

- If the function translated vertically by k units down , then the new

function is $g(x)=a(b)^{x}-k$

* Lets solve the problem

∵ f(x) is an exponential function

∵ Points (0 , 1) , (1 , 10) , (2 , 100) belong to f(x)

- g(x) is the image of f(x) after translation

∵ Points (3 , 1) , (4 , 10) , (5 , 100) belong to g(x)

∵ point (0 , 1) on f(x) becomes (3 , 1) on g(x)

∵ point (1 , 10) on f(x) becomes (4 , 10) on g(x)

∵ point (2 , 100) on f(x) becomes (5 , 100) in g(x)

∵ All the y-coordinates of the points on the function f(x) are the same

with the y-coordinates of the points on the function g(x)

∴ There is no vertical translation

∵ The x-coordinates of the points on the function f(x) are added by

3 units to give the x-coordinates of the points on the function g(x)

∴ f(x) is translated 3 units to the right

∵ $f(x)=(10)^{x}$

∴ $g(x)=(10)^{x-3}$

- Look to the attached graph for more understand

# Red graph represents f(x)

# Blue graph represents g(x)

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