Zeroes of a function are used because they are another way to talk about solving an equation, which is a main goal in algebra. If we want to solve an equation like "x"2 = 1, then we can subtract the right-hand side of the equation from both sides, in this case 1. Whatever we get on the left-hand side, in this case "x"2 − 1, can be called a function "f"(x). The right-hand side has to be zero, because we subtracted it from itself. So "f"(x) = 0. Finding the zeroes of this function is the same as solving this equation. In the paragraph before, the zeroes of this function are +1 and −1, so they are the solutions of this equation. We got this equation by subtracting the same thing from both sides, so we also have solutions to the equation we started with, in this case "x"2 = 1. More generally, if we could find zeroes of functions, we could solve any equation.= = = Zoology = = =
z iə ɹ oʊ z WORD_BOUNDARY ə v ə WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY ɑ ɹ WORD_BOUNDARY j uː z d WORD_BOUNDARY b ɪ k ʌ z WORD_BOUNDARY ð eɪ WORD_BOUNDARY ɑ ɹ WORD_BOUNDARY ʌ n ʌ ð ə ɹ WORD_BOUNDARY w eɪ WORD_BOUNDARY t ə WORD_BOUNDARY t ɔ k WORD_BOUNDARY ʌ b aʊ t WORD_BOUNDARY s ɑ l v ɪ ŋ WORD_BOUNDARY ʌ n WORD_BOUNDARY ɪ k w eɪ ʒ ə n WORD_BOUNDARY w ɪ t̠ʃ WORD_BOUNDARY ɪ z WORD_BOUNDARY ʌ WORD_BOUNDARY m eɪ n WORD_BOUNDARY ɡ oʊ l WORD_BOUNDARY ɪ n WORD_BOUNDARY æ l d̠ʒ ɪ b ɹ ə WORD_BOUNDARY ɪ f WORD_BOUNDARY w iː WORD_BOUNDARY w ɔ n t WORD_BOUNDARY t ə WORD_BOUNDARY s ɑ l v WORD_BOUNDARY ʌ n WORD_BOUNDARY ɪ k w eɪ ʒ ə n WORD_BOUNDARY l aɪ k WORD_BOUNDARY ɛ k s WORD_BOUNDARY t uː WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY w ʌ n WORD_BOUNDARY ð ɛ n WORD_BOUNDARY w iː WORD_BOUNDARY k æ n WORD_BOUNDARY s ʌ b t ɹ æ k t WORD_BOUNDARY ð ə WORD_BOUNDARY ɹ aɪ t h æ n d WORD_BOUNDARY s aɪ d WORD_BOUNDARY ʌ v ð ɪ WORD_BOUNDARY ɪ k w eɪ ʒ ə n WORD_BOUNDARY f ɹ ʌ m WORD_BOUNDARY b oʊ θ WORD_BOUNDARY s aɪ d z WORD_BOUNDARY ɪ n WORD_BOUNDARY ð ɪ s WORD_BOUNDARY k eɪ s WORD_BOUNDARY w ʌ n WORD_BOUNDARY w ʌ t ɛ v ə ɹ WORD_BOUNDARY w iː WORD_BOUNDARY ɡ ɛ t WORD_BOUNDARY ɔ n ð ə WORD_BOUNDARY l ɛ f t h æ n d WORD_BOUNDARY s aɪ d WORD_BOUNDARY ɪ n WORD_BOUNDARY ð ɪ s WORD_BOUNDARY k eɪ s WORD_BOUNDARY ɛ k s WORD_BOUNDARY t uː WORD_BOUNDARY m aɪ n ə s WORD_BOUNDARY w ʌ n WORD_BOUNDARY k æ n WORD_BOUNDARY b iː WORD_BOUNDARY k ɔ l d WORD_BOUNDARY ʌ WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY ɛ f WORD_BOUNDARY ɛ k s WORD_BOUNDARY ð ə WORD_BOUNDARY ɹ aɪ t h æ n d WORD_BOUNDARY s aɪ d WORD_BOUNDARY h ʌ z WORD_BOUNDARY t ə b i WORD_BOUNDARY z iə ɹ oʊ WORD_BOUNDARY b ɪ k ʌ z WORD_BOUNDARY w iː WORD_BOUNDARY s ʌ b t ɹ æ k t ɪ d WORD_BOUNDARY ɪ t WORD_BOUNDARY f ɹ ʌ m WORD_BOUNDARY ɪ t s ɛ l f WORD_BOUNDARY s oʊ WORD_BOUNDARY ɛ f WORD_BOUNDARY ɛ k s WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY z iə ɹ oʊ WORD_BOUNDARY f aɪ n d ɪ ŋ WORD_BOUNDARY ð ə WORD_BOUNDARY z iə ɹ oʊ z WORD_BOUNDARY ʌ v WORD_BOUNDARY ð ɪ s WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY ɪ z WORD_BOUNDARY ð ə WORD_BOUNDARY s eɪ m WORD_BOUNDARY æ z WORD_BOUNDARY s ɑ l v ɪ ŋ WORD_BOUNDARY ð ɪ s WORD_BOUNDARY ɪ k w eɪ ʒ ə n WORD_BOUNDARY ɪ n ð ə WORD_BOUNDARY p æ ɹ ə ɡ ɹ æ f WORD_BOUNDARY b ɪ f ɔ ɹ WORD_BOUNDARY ð ə WORD_BOUNDARY z iə ɹ oʊ z WORD_BOUNDARY ʌ v WORD_BOUNDARY ð ɪ s WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY ɑ ɹ WORD_BOUNDARY p l ʌ s WORD_BOUNDARY w ʌ n WORD_BOUNDARY æ n d WORD_BOUNDARY m aɪ n ə s WORD_BOUNDARY w ʌ n WORD_BOUNDARY s oʊ WORD_BOUNDARY ð eɪ WORD_BOUNDARY ɑ ɹ WORD_BOUNDARY ð ə WORD_BOUNDARY s ə l uː ʃ ə n z WORD_BOUNDARY ʌ v WORD_BOUNDARY ð ɪ s WORD_BOUNDARY ɪ k w eɪ ʒ ə n WORD_BOUNDARY w iː WORD_BOUNDARY ɡ ɑ t WORD_BOUNDARY ð ɪ s WORD_BOUNDARY ɪ k w eɪ ʒ ə n WORD_BOUNDARY b aɪ WORD_BOUNDARY s ʌ b t ɹ æ k t ɪ ŋ WORD_BOUNDARY ð ə WORD_BOUNDARY s eɪ m WORD_BOUNDARY θ ɪ ŋ WORD_BOUNDARY f ɹ ʌ m WORD_BOUNDARY b oʊ θ WORD_BOUNDARY s aɪ d z WORD_BOUNDARY s oʊ WORD_BOUNDARY w iː WORD_BOUNDARY ɔ l s oʊ WORD_BOUNDARY h æ v WORD_BOUNDARY s ə l uː ʃ ə n z WORD_BOUNDARY t ə WORD_BOUNDARY ð ɪ WORD_BOUNDARY ɪ k w eɪ ʒ ə n WORD_BOUNDARY w iː WORD_BOUNDARY s t ɑ ɹ t ɪ d WORD_BOUNDARY w ɪ ð WORD_BOUNDARY ɪ n WORD_BOUNDARY ð ɪ s WORD_BOUNDARY k eɪ s WORD_BOUNDARY ɛ k s WORD_BOUNDARY t uː WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY w ʌ n WORD_BOUNDARY m ɔ ɹ WORD_BOUNDARY d̠ʒ ɛ n ə ɹ ɹ ə l i WORD_BOUNDARY ɪ f WORD_BOUNDARY w iː WORD_BOUNDARY k ʊ d WORD_BOUNDARY f aɪ n d WORD_BOUNDARY z iə ɹ oʊ z WORD_BOUNDARY ʌ v WORD_BOUNDARY f ʌ ŋ k ʃ ə n z WORD_BOUNDARY w iː WORD_BOUNDARY k ʊ d WORD_BOUNDARY s ɑ l v WORD_BOUNDARY ɛ n i WORD_BOUNDARY ɪ k w eɪ ʒ ə n WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY z uː ɑ l ə d̠ʒ i WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY