Questions tagged [graphing-functions]
For questions regarding the plotting or graphing of functions. For questions about the kinds of graphs with vertices and edges, use the (graph-theory) tag instead.
5,127 questions
3 votes
3 answers
189 views
Finding a function for $\sin(x)\sec(y) = \sin(y) + \sec(x)$
While messing around on desmos, I discovered the function $$\sin(x)\sec(y)=\sin(y)+\sec(x)$$ which appears as a warped sinusoid glide-reflected to fill the plane (graph in Desmos). Each of these ...
2 votes
0 answers
62 views
Copeland-Erdős constant random walk
WOW! Here are two photos of Copeland-Erdős constant with first 500 digits and first 4000 digits. In Copeland-Erdős constant all prime numbers are presented in order in decimal so $0....
13 votes
1 answer
1k views
Why do these valleys in $LCM(P_n - 1, P_n + 1) \bmod n$ exist and are they random?
I wanted to see what kind of properties the numbers just one more or one less than primes would have. I supposed $P_n$ was the $n^{th}$ prime and obtained two numbers from it, $(P_n-1)$ and $(P_n+1)$. ...
- 149
2 votes
2 answers
73 views
What is the cartesian equation for the graph of the parametric curve $(x,y)= ( t^{\frac{1}{1-t}},\, t^{\frac{t}{1-t}}) $?
The parametric curve $$ \left( t^{\frac{1}{1-t}},\, t^{\frac{t}{1-t}}\right) $$ for $t \in (0,1)\cup(1,\infty)$ traces out the points on the graphs of $y = x^t$ which are furthest from the line $y = x$...
- 7,626
0 votes
0 answers
59 views
Conditions for the intersection of two weird functions
(From a question at HNUE High School for the Gifted) Let $$f(x) = |a|^{bx}-|b|^{ax}\\g(x) = abx$$Such that $a$ and $b$ are real numbers. What are the conditions needed for $f(x)$ and $g(x)$ to ...
- 11
2 votes
1 answer
57 views
Graphically Self-Referential Function
Does there exist a function $f(x)$ whose graph, when plotted on the Cartesian coordinate plane, visually looks like the expression of the function itself? To explain this more thoroughly, even though ...
- 166
0 votes
1 answer
73 views
What does a 3D plot of a quadratic look like if the z-axis represents imaginary input values?
I recently saw this video about factoring any quadratic expression without guessing and checking. The implication, that I probably should have got sooner, is that $f(x) = 0$ then always have a ...
- 103
0 votes
1 answer
64 views
What am I doing wrong with this Taylor Series expansion
I am trying to find the Taylor Series expansion for sin(x) at $\frac{π}{2}$. I found the series and confirmed it with the key, however when I graph it my solution seems to be shifted down 1 and adding ...
- 77
38 votes
3 answers
1k views
Given the graph $y=x^4$, can we construct the $y$-axis using only a straightedge and a compass?
This is a question my friend raised and we have had difficulty solving it. Suppose that the graph of the polynomial function $f(x)=x^4$ is drawn on a plane. Can we construct the $y$-axis of this ...
- 933
0 votes
1 answer
41 views
Is it possible to draw 2d density plot only knowing totals in any cross line
So we see from the density plot that the most dense part happens to be intersection of the x, y histograms where the highest bar meet. But suppose we only have the x, y histograms, I think it's not ...
- 203
5 votes
1 answer
72 views
Plotting functions in a way consistent with measure theory
So as far as I understand, modern plotting software work by filling every pixel that intersects the graph of the function. While this works pretty well for contineous functions, it is clear why this ...
- 333
0 votes
0 answers
57 views
How to plot the 1-D Wave Equation solution given $u(0,t)=0=u(L,t)$ and $u(x,0)=f(x)$ and $u'(x,0)=g(x)$？
My goal is to create a plot that I can input different initial conditions into and see the effect while sliding the $t$ (time) parameter. But my formulas don't seem to be producing the correct result, ...
- 51
0 votes
2 answers
97 views
How to tell whether a quartic equation has only one turning point?
I want to sketch the equation $y=(x^2+3x+12)(x+1)(3x-1)$, which can be deduced as a quartic with roots $-1$ and $\frac13$ and a $y$-intercept of $-12$. I imagined the equation as having three turning ...
- 25
0 votes
1 answer
104 views
Logarithmic function, simplification of an expression
The formula for a logarithmic function is as follows: $$f(x) = -3\log(6x+11)-9$$ The question is: Suppose b is a number for which both $b$ and $10b + \frac{33}{2}$ are in the domain of $f(x)$ (which ...
-3 votes
1 answer
108 views
Is $f(x)=\max[\{x+1\}, \{5-x\}]$, where $\{x\}$ is fractional part of $x$, periodic or not in $[-2,2]$? [closed]
It obviously seems periodic, I am getting a period of 1, I have made the graph many times, both on paper and on Desmos. I asked Grok and Gemini, both are saying this is a periodic graph, but the ...
- 1