On the real number line, the real number zero is the coordinate of the .

Homework 9 Calder Sheagren 1 a) Claim: f : R ! R;f(x) = 17 is continuous at x = 9: 0 Proof. Take an arbitrary ▯ > 0. Let ▯ = ▯. Then, for all jx ▯ x j < ▯; jf(x) ▯ f(x )j = 0 0 j17 ▯ 17j = 0 < ▯ = ▯. b) Claim: g : R ! R;g(x) = x is continuous at x = 9: 0 Proof. Take an arbitrary ▯ > 0. Let ▯ = ▯. Then, for all jx ▯ x j < ▯; jg(0) ▯ g(x )j = 0 jx ▯ 9j < ▯ = ▯. 2 c) Claim: h : R ! R;h(x) = x + 2 is continuous at x = 9: 0 2 Proof. Take an arbitrary ▯ > 0. Let ▯ = ▯ +18▯. Then, for all jx▯x j < ▯; j