Mother Functions
Answer: SOFTWARE
Brian Zhang

Solving each cryptic clue yields the name of a standard mathematical function. Counting the highlighted letters in the grid reveals that there are eight $y$'s, eight $x$'s, and eight distinct greek letters. This, along with the flavortext and title, points towards needing to find eight curves within the word search, each of which contains a set of the triplets.

We can initially approach the word search like any other word search. Looking around the grid we can find a couple words like "equals" in the absolute value curve or the "divided" in the tangent curve. Attempting to trace linearly outwards from these two words and finding gibberish can lead to the realization that the words can be nonlinear on the grid. Continuing these curves outwards yields us function formulas which describe the shape of the curve on the word search.

We can find the other curves by starting from a highlighted letter, and searching outwards. What is helpful in doing this word search is realizing that the ordering of the greek letters corresponds to the order of the functions given by the cryptics. Knowing that the $\beta$ corresponds to a log curve or that the $\alpha$ corresponds to a sine curve makes searching for them much easier.

For extraction, we have to calculate the value of the given greek for each function using the knowledge that the distance between letters is 1 unit. For instance, the radius of the circle is 6 units. Thus $\theta = 6$ satisfies $\theta^2 = x^2 + y^2$. Having done this, we can use the calculated greek values to index into the function name.

Cryptics Function Formula Greek Extract
Latin without speaker's symptom (4) SINE $y = 4 \alpha \sin (\frac{\pi}{4} * x)$ $\alpha = 1$ S
Journal of a long Orlando getaway at first (3) LOG $y = 10 \beta \log_{10} x$ $\beta = 2$ O
Knock down flipped roof to admit loss (5) FLOOR $y = \gamma \lfloor x \rfloor$ $\gamma = 1$ F
Sunburnt guy's digression (7) TANGENT $y = \tan (\frac{1}{\delta} \pi x)$ $\delta = 7$ T
Confused Oshawott is serrated (8) SAWTOOTH $y = \frac{\epsilon^2}{\pi} \arctan \cot (\frac{\pi x}{3})$ $\epsilon = 3$ W
Perfect core is the essence of choir instrument (8) ABSOLUTE $y = \zeta |x|$ $\zeta = 1$ A
Endless exaggeration with a conic section (9) HYPERBOLA $\eta^2 = x^2 - y^2$ $\eta = 5$ R
Chip recalled odd acquaintances (6) CIRCLE $\theta ^2 = x^2 + y^2$ $\theta = 6$ E

Here's a more in depth explanation of the cryptics, in order.
  • SINE "sign": The latin word for without is SINE. "Speaker's" is a homophone indicator and "sign" is a symptom.
  • LOG inits: The definition here is "journal". Taking the initial letters of "long Orlando getaway" yields LOG and is clued by "at first".
  • F(L)OOR<: The definition is "knock down". A "flipped roof" is one that is reversed, i.e. FOOR. Finally, "admit loss" adds an L.
  • TAN+GENT: The definition is "digression". "Sunburnt" is TAN and "guy" is GENT.
  • SAWTOOTH*: The definition is "serrated". "Confused" is an anagram indicator and "Oshawott" is an anagram of SAWTOOTH.
  • ABS+_O_+LUTE: "Perfect" is our definition. Your core is your ABS. The essence letter of "choir" is O, as that's the middle letter. LUTE is an instrument.
  • HYPERBOL(-e)+A: The definition is "conic section". "Endless" means that we lop off the last letter of HYPERBOLe, which is an exaggeration. Then we add an A.
  • C_I_R_C_L_E_: Acquaintances are a social CIRCLE. Our word hides in every other, i.e. odd, letter of "Chip recalled".