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Ответ:
Step-by-step explanation:
* Lets explain how to solve the problem
- The form of the exponential function is
, 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}](/tpl/images/0210/7677/15daa.png)
- If the function translated horizontally by h units to the left , then
the new function is![g(x)=a(b)^{x+h}](/tpl/images/0210/7677/56797.png)
- If the function translated vertically by k units up , then the new
function is![g(x)=a(b)^{x}+k](/tpl/images/0210/7677/1135f.png)
- If the function translated vertically by k units down , then the new
function is![g(x)=a(b)^{x}-k](/tpl/images/0210/7677/6c21d.png)
* 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}](/tpl/images/0210/7677/aec4a.png)
∴![g(x)=(10)^{x-3}](/tpl/images/0210/7677/85a81.png)
- Look to the attached graph for more understand
# Red graph represents f(x)
# Blue graph represents g(x)