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What exponential function, g(x), will translate the original function, = 3.5^ − 4, 4 units to the right and 6 units up?

What exponential function, g(x), will translate the original function, = 3.5^ − 4, 4 units-example-1
User Fbucek
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1 Answer

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Given:


f(x)=3.5^x-4

Required:

We need to find the function g(x) that translates the function f(x) 4 units right and 6 units up.

Step-by-step explanation:

In the exponential function f(x-4) shift the function f(x) 4 units right,

Replace x = x-4 in the given function f(x).


f(x-4)=3.5^(x-4)-4

Add 6 to both sides of the equation to life the function f(x) up by 6 units.


f(x-4)+6=3.5^(x-4)-4+6
f(x-4)+6=3.5^(x-4)+2


Let\text{ }g(x)=f(x-4)+6.

We get


g(x)=3.5^(x-4)+2

Final answer:


g(x)=3.5^(x-4)+2

What exponential function, g(x), will translate the original function, = 3.5^ − 4, 4 units-example-1
What exponential function, g(x), will translate the original function, = 3.5^ − 4, 4 units-example-2
User Robear
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3.0k points