Polynomial and Rational Functions

In a proportional relationship where $y$ is multiplied by a constant to equal $x$ between two variables $y$ and $x$, what is the constant referred to as in this context of a proportionality constant?

When analyzing $h(x)=\ln|x-5|$ near $x=5$, what type of discontinuity should students expect to find?

If function $f$ has an inverse denoted by $f^{-1}$ and the point $(3, 7)$ lies on the graph of $f$, which point must lie on the graph of $f^{-1}$?

What kind of discontinuity occurs if a single point is removed from the graph of a continuous function?

Which type of model best describes a scenario where the cooling temperature of a cup of coffee in a room is proportional to the difference between the coffee's temperature and room temperature?

If a horizontal line intersects a graph more than once, what property does the graph lack?

If you plot a set of points where each x-value has exactly one corresponding y-value, what are you most likely graphing?

For modeling the depreciation of a car’s value over time assuming constant annual decrease, which type of mathematical model is most appropriate?

Which of the following functions is continuous at $x = 3$?

Given a multi-phase project where each phase can be modeled by either a linear, quadratic, or exponential function, which function type would be best to model the diminishing returns in productivity over time as employees become fatigued?