What function represents a reflection f(x)=3/7(2)^x over the x-axis

The given function is
f(x) = (3/7) 2^x
And it is to be reflected over the x-axis. This means that the function will have an opposite sign or -f(x). The resulting function after the reflections is
-f(x) = -(3/7) 2^x

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MrRoyal MrRoyal · Answer 2 · 2021-11-02T09:36:37-04:00

When a function is reflected, it must be reflected over a line.

The function that represents a reflection over the x-axis is: \(\mathbf{g(x) = -\frac{3}{7}(2)^x}\)

The function is given as:

\(\mathbf{f(x) = \frac{3}{7}(2)^x}\)

The rule of reflection over the x-axis is:

\(\mathbf{(x,y) \to (x,-y)}\)

So, we have:

\(\mathbf{g(x) = -f(x)}\)

This gives:

\(\mathbf{g(x) = -\frac{3}{7}(2)^x}\)

Hence, the function that represents a reflection over the x-axis is: \(\mathbf{g(x) = -\frac{3}{7}(2)^x}\)