Functions Involving Parameters, Vectors, and Matrices

How would parametric functions represent x and y?

If the position of an object is given by parametric equations $x(t)=\sin(t)+\cos(t)$ and $y(t)=\sin(t)-\cos(t)$, what is $\frac{dy}{dx}$ at time $t=\frac{\pi}{4}$?

What describes the behavior of a function that alters its direction abruptly at certain points on its graph?

What is the first step to eliminate the parameter in the parametric equations $x = 3t + 2$ and $y = 2t - 5$?

When translating between Cartesian equations and parametric forms, which element is typically replaced with expressions involving 't'?

In parametric functions, what typically represents the independent parameter?

What do you need to find in order to create a table that will help you graph a set of parametric equations?

For a projectile modeled by parametric equations $x(t) = v_{0} \cos(\theta)t$ and $y(t) = v_{0} \sin(\theta)t - \left( \frac{g}{2} \right)t^{2}$, where $g$ represents gravity, what affects the time it takes for the projectile to reach maximum height?

If a parameter 't' in a parametric function is described as being continuous, what type of number must 't' be?

For a space probe traveling along a path described by $x(t)=e^{-t} \cos(t)$, $y(t)=e^{-t} \sin(t)$, at what time 't' is its speed minimized within the interval (0, ∞)?