Determine whether the function below is an even function, an odd function, both, or neither. $$ f(x)=\frac{3}{4} x $$ odd function even function belther even nor odd both even and odd

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To determine whether the function $$ f(x) = \frac{3}{4}x $$ is even, odd, both, or neither, let's analyze it based on the definitions of even and odd functions.

### Definitions:
- **Even Function:** A function $$ f $$ is even if $$ f(-x) = f(x) $$ for all $$ x $$ in its domain.
- **Odd Function:** A function $$ f $$ is odd if $$ f(-x) = -f(x) $$ for all $$ x $$ in its domain.

### Applying the Definitions:
1. **Check if $$ f $$ is Even:**
   $$
   f(-x) = \frac{3}{4}(-x) = -\frac{3}{4}x
   $$
   Since $$ f(-x) = -\frac{3}{4}x $$ is **not** equal to $$ f(x) = \frac{3}{4}x $$, the function is **not even**.

2. **Check if $$ f $$ is Odd:**
   $$
   f(-x) = \frac{3}{4}(-x) = -\frac{3}{4}x = -f(x)
   $$
   Here, $$ f(-x) = -f(x) $$, which satisfies the condition for an **odd function**.

### Conclusion:
The function $$ f(x) = \frac{3}{4}x $$ is an **odd function**.

**Answer:**  
odd function
The function $$ f(x) = \frac{3}{4}x $$ is an **odd function**.

Determine whether the function below is an even function, an odd function, both, or neither. \[ f(x)=\frac{3}{4} x \] odd function even function belther even nor odd both even and odd

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