- Utilize arrow notation to specify the behavior of rational functions.
- Find the domains of rational functions.
- Identify vertical and horizontal asymptotes.
- Identify slant asymptotes.
- Graph rational functions.
Physics – Optical Lens Systems
A physics lab is studying how light behaves through different lens systems. When two converging lenses are placed at varying distances apart, the effective focal length of the compound system changes dramatically. The effective focal length [latex]f(d)[/latex] (in cm) depends on the distance [latex]d[/latex] (in cm) between the lenses according to:
[latex]f(d) = \frac{12d}{d^2 - 16}[/latex]
Optical System Analysis
Let’s analyze this lens system to understand how distance affects focusing behavior and identify critical separation distances.
Consider the function: [latex]f(d) = \frac{12d}{d^2 - 16}[/latex].
Determine where the lens system is undefined.
Again, consider the function: [latex]f(d) = \frac{12d}{d^2 - 16}[/latex].Analyze the long-distance behavior of the lens system.