Continuity at a point means that you can draw the function at that point without lifting up your pencil. Or in more technical terms, a small change in x produces only a small change in f(x)<\/p>\n
In order for a function to be continuous at a point it must follow three criteria: 1) f(A) must be defined 2) f(x) has a limit as x approaches A from both direction 3) the limit as x approaches A is actually equal to f(A)<\/p>\n
To visualize this, below is a continuous graph at point A. Notice how you could draw this without picking up your pencil. <\/p>\n
Now below is a graph that is discontinuous for multiple reasons. Notice how you would have to pick up your pencil to draw this graph. <\/p>\n","protected":false},"excerpt":{"rendered":"
Continuity at a point means that you can draw the function at that point without lifting up your pencil. Or in more technical terms, a small change in x produces only a small change in f(x) In order for a Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-143881","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/143881","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=143881"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/143881\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=143881"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=143881"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=143881"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}