\# $$ \quad $$ Which function is decreasing with a. $$ f(x)=2^{x}+8 $$ b. $$ f(x)=\left(\frac{1}{2}\right)^{x}+8 $$ c. $$ f(x)=-2(4)^{x}+8 $$ d. $$ f(x)=-2\left(\frac{1}{4}\right)^{x}+8 $$

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To determine which function is decreasing, we need to analyze the behavior of each function as $$ x $$ increases.

1. **Function a: $$ f(x) = 2^{x} + 8 $$**
   - The term $$ 2^{x} $$ is an exponential function that increases as $$ x $$ increases. Therefore, $$ f(x) $$ is increasing.

2. **Function b: $$ f(x) = \left(\frac{1}{2}\right)^{x} + 8 $$**
   - The term $$ \left(\frac{1}{2}\right)^{x} $$ is an exponential function that decreases as $$ x $$ increases. Therefore, $$ f(x) $$ is decreasing.

3. **Function c: $$ f(x) = -2(4)^{x} + 8 $$**
   - The term $$ -2(4)^{x} $$ is a negative exponential function that decreases as $$ x $$ increases. Therefore, $$ f(x) $$ is also decreasing.

4. **Function d: $$ f(x) = -2\left(\frac{1}{4}\right)^{x} + 8 $$**
   - The term $$ -2\left(\frac{1}{4}\right)^{x} $$ is a negative exponential function that increases as $$ x $$ increases. Therefore, $$ f(x) $$ is increasing.

### Conclusion:
The functions that are decreasing are:
- **Function b: $$ f(x) = \left(\frac{1}{2}\right)^{x} + 8 $$**
- **Function c: $$ f(x) = -2(4)^{x} + 8 $$**

Thus, both b and c are decreasing functions.
Functions b and c are decreasing.

# Which function is decreasing with
a.
b.
c.
d.

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