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Alex17521 [72]
3 years ago
13

Which function represents g(x), a reflection of f(x)=4(1/2)^x across the x-axis?

Mathematics
1 answer:
prohojiy [21]3 years ago
8 0

Answer:

g(x)=-4(\frac{1}{2})^x

Step-by-step explanation:

Given:

The parent function is given as:

f(x)=4(\frac{1}{2})^x

The function g(x) is a reflection of the parent function about the x-axis.

Now, in order to find the function g(x), we need to use the rules of function transformations.

As per transformation rules, when a function is reflected about the x-axis, the function rule is given as:

f(x)\to-f(x)

So, the new function or the reflected function is the negative of the original function.

Therefore, the reflected function g(x) is given as:

g(x)=-f(x)\\\\g(x)=-4(\frac{1}{2})^x

Hence, the function that represents the reflection of the given function across the x-axis is g(x)=-4(\frac{1}{2})^x

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