Let's analyze the given transformed function step-by-step.
1. Understand the Function [tex]\( m(x) \)[/tex]:
The given function is [tex]\( m(x) = \frac{4}{4} \pi^3 + 6 \)[/tex].
2. Simplify the Expression:
[tex]\(\frac{4}{4}\)[/tex] simplifies to 1. Thus, the function simplifies to [tex]\( m(x) = 1 \cdot \pi^3 + 6 \)[/tex], which simplifies further to [tex]\( m(x) = \pi^3 + 6 \)[/tex].
3. Evaluate the Constant Term:
The term [tex]\(\pi^3\)[/tex] is a constant value. According to the calculation, [tex]\(\pi^3 \approx 31.006276680299816\)[/tex].
4. Add the Constant Value of 6:
Adding 6 to [tex]\(\pi^3\)[/tex], we get [tex]\( \pi^3 + 6 \approx 31.006276680299816 + 6 \approx 37.00627668029982 \)[/tex].
5. Consider the Behavior as [tex]\( x \)[/tex] Approaches Infinity:
Since [tex]\( m(x) = \pi^3 + 6 \)[/tex] is a constant function, the value of [tex]\( m(x) \)[/tex] does not change with [tex]\( x \)[/tex]. Therefore, as [tex]\( x \)[/tex] approaches positive or negative infinity, [tex]\( m(x) \)[/tex] remains the same.
So, we can conclude:
- As [tex]\( x \)[/tex] approaches positive infinity, [tex]\( m(x) \)[/tex] approaches 37.00627668029982.
- As [tex]\( x \)[/tex] approaches negative infinity, [tex]\( m(x) \)[/tex] approaches 37.00627668029982.
Thus, the final answers are:
[tex]\[ \boxed{37.00627668029982} \][/tex] for both cases.
