In calculus, we define a function f to be continuous at a real number a provided that for every " > 0, there exists a ı > 0 such that if jx aj < ı, thenjf .x/f .a/j<".
Note: The symbol " is the lowercase Greek letter epsilon, and the symbol ı is the lowercase Greek letter delta.
Complete each of the following sentences using the appropriate symbols for quantifiers:
(a) Afunctionf
(b) Afunctionf
Complete the following sentence in English without using symbols for quan- tifiers:
(c) Afunctionf

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality