Graphing letter A

Question

How can I use two functions to graph the letter $A$?

I need two functions $x(t)$ and $y(t)$ on $0\leq t\leq 1$ so that $(x(t),y(t))$ represents the alphabet$A$.

I'm thinking of a $|x|$ and $x$. Can anyone show it to me on a graphing software here?

Answer 1

If you are satisfied with the NASA font, you can use $y=4-4|x|$ for $-1\le x \le 1$. It has no crossbar.

Is it given that the two functions are $x(t)$ and $y(t)?$ rather than $y_1(x)$ and $y_2(x)?$ The fact that $A$ doesn't satisfy the vertical line rule raises the question in my mind. You can add a function to the above to get the cross bar (in the sense of union, not addition).

Added: It might not meet your needs, but I would then suggest $$x=\begin {cases} t&0\le t \le 1\\2-t&1 \lt t \le 2\end {cases}\\ y=\begin{cases} 4t&0 \le t \lt \frac 12\\4-4t&\frac 12 \lt t \le 1\\ 4t-4&1\lt t \le \frac 54\\\frac 12&\frac 54 \lt t \le \frac 74\\4(2-t)&\frac 74 \lt t \le 2\end{cases}$$ where $[0,1]$ traces the $\wedge$ and $[1,2]$ goes back up the wedge, across the crossbar, and down the wedge again

Answer 2

To make the two sharp lines on the sides of the $A$, we use the absolute value of $x$: $|x|$. But that's upside-down, making a shape like this: $\lor$. So if we just flip that with a negative sign,$-(|x|)$, we get something like this: $\land$.

Then we just need a constant function for the horizontal bar between the two lines. In my example, $f(x)=0.5$ will work.

Here's my plot. If you don't want the horizontal bar extending past the sides of the $A$, then it gets a bit trickier.