This lesson has two major parts, easy and advanced. Whenever you need to draw a graph, you always need to follow the following guidelines. How to plot a nice graph with sweaty shaky hands Determine …

Jan 13, 2011 · To convert that to a function, we find $t$ as a function of $x$ and plug that into $Y$ as a function of $t$. This is possible with some equations, such as $f (t)=t^2$ or $f (t)=\dfrac 1t$.

A function doesn't have to be differentiable anywhere for it to be 1 to 1. Consider the function given by f (1)=2, f (2)=3. It is defined only at two points, is not differentiable or continuous, but is one to one.

Jul 21, 2018 · And lastly, if a line in a graph gets very close to an "asymptote" on one side of the "asymptote", then veers completely away from the "asymptote" after passing through it, can this …

Jan 9, 2023 · I'm self-studying calculus by using Khan Academy, and I find myself consistently getting problems wrong where I'm asked to determine concavity from a graph or inflection points from a graph.

Well after doing some example questions, the line of the function sometimes passed the horizontal asymptote. Just graph the function I gave as an example (the answer key shows it passed through …

A function is not the same as its graph, nor is it the same as its level curves. I think it gets even worse for my poor Calc III students, who have to integrate functions of three variables over three …

Mar 18, 2017 · There are a lot of different tools to graph online, by example I discovered today the library plotly that can be used in many programming languages (and online too!).

If the graph of a function are a just a set of ordered pairs, then the graph of the graph of a function are the actual geometric points in the space $\mathbb R^n \times \mathbb R $ (their coordinates are …

Where do you have your three-item list from, especially the claim that it is exhaustive? What about $\frac1x\sin (1/x)$ type of functions?