Given , find
a
b
c
d
Check It

To find , we substitute into the function:

So the answer is .

Now, let’s delve deeper into how this function behaves!

This function represents a rational expression, which often has interesting characteristics like asymptotes and intercepts due to its polynomial nature in both the numerator and denominator. As approaches , the denominator becomes zero; hence, we have a vertical asymptote there, indicating that the function values will skyrocket or plunge depending on the direction of approach!

Additionally, understanding rational functions like can be super useful in various real-world scenarios, such as analyzing rates in physics or economics. For instance, if you were to model the efficiency of a machine depending on its operating speed, a similar rational function might come into play, revealing how changes in input yield different outputs!