The function $$ y=\left(\frac{1}{2} ight)^{x} $$ is the parent function of which of the following? (1 point) $$ \begin{array}{l}f(x)=-(2)^{x} \ f(x)=-5\left(\frac{1}{2} ight)^{x} \ f(x)=-5 x^{2} \ f(x)=x^{\frac{1}{2}}\end{array} $$

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The function $$ y=\left(\frac{1}{2}ight)^{x} $$ is the parent function of which of the following? (1 point) $$ \begin{array}{l}f(x)=-(2)^{x} \ f(x)=-5\left(\frac{1}{2}ight)^{x} \ f(x)=-5 x^{2} \ f(x)=x^{\frac{1}{2}}\end{array} $$

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The function $$ y = \left(\frac{1}{2}\right)^{x} $$ is an exponential decay function. To determine which of the given functions is related to this parent function, we can analyze each option:

1. $$ f(x) = -(2)^{x} $$: This is an exponential growth function (with a negative sign in front, it reflects the graph across the x-axis). It is not related to the decay function.

2. $$ f(x) = -5\left(\frac{1}{2}\right)^{x} $$: This is also an exponential decay function, but it is vertically stretched by a factor of 5 and reflected across the x-axis due to the negative sign. This function is related to the parent function $$ y = \left(\frac{1}{2}\right)^{x} $$.

3. $$ f(x) = -5 x^{2} $$: This is a quadratic function, which is not related to the exponential function.

4. $$ f(x) = x^{\frac{1}{2}} $$: This is a square root function, which is also not related to the exponential function.

The function that is related to the parent function $$ y = \left(\frac{1}{2}\right)^{x} $$ is:

**$$ f(x) = -5\left(\frac{1}{2}\right)^{x} $$**.
The function related to the parent function $$ y = \left(\frac{1}{2}\right)^{x} $$ is $$ f(x) = -5\left(\frac{1}{2}\right)^{x} $$.

The function is the parent function of which of the following? (1 point)

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