{"id":4692,"date":"2022-09-01T12:29:34","date_gmt":"2022-09-01T10:29:34","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/funkce-priklad-4\/"},"modified":"2022-09-01T12:29:34","modified_gmt":"2022-09-01T10:29:34","slug":"funkce-priklad-4","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/funkce-priklad-4\/","title":{"rendered":"Funkce &#8211; p\u0159\u00edklad 4"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong><\/p>\n<p>Grafy funkc\u00ed <em><strong>f<\/strong><\/em> a <em><strong>g<\/strong><\/em> jsou p\u0159\u00edmky. Graf funkce<strong><em> f<\/em><\/strong> proch\u00e1z\u00ed po\u010d\u00e1tkem <em><strong>O<\/strong> <\/em>a bodem <em><strong>A<\/strong><\/em>. Grafy funkc\u00ed <strong><em>f<\/em><\/strong> a <em><strong>g<\/strong><\/em> se prot\u00ednaj\u00ed v bod\u011b <strong><em>B<\/em><\/strong>.<\/p>\n<p style=\"text-align: center\" data-mce-style=\"text-align: center;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone  wp-image-4691\" src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/funkce-4-300x157.png\" alt=\"\" width=\"466\" height=\"244\" data-mce-src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/funkce-4-300x157.png\" srcset=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/funkce-4-300x157.png 300w, https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/funkce-4.png 530w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>a) <strong>Zapi\u0161te p\u0159edpis funkce <em>f<\/em>.<\/strong><br \/>b) <strong>Zapi\u0161te obecnou rovnici p\u0159\u00edmky, kter\u00e1 je grafem funkce <em>g<\/em><\/strong>.<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>a) <em>P\u0159edpis funkce f<\/em><\/p>\n<p>O [0; 0] A [10; 5]<br \/>1) Funkce je d\u00e1na p\u0159edpisem<br \/>$$y = ax + b$$<br \/>2) Dosad\u00edme za x a y sou\u0159adnice O a vyjde n\u00e1m kolik je b<br \/>$$0 = 0\\cdot a + b \u21d2 b = 0$$<br \/>3) Nyn\u00ed dosad\u00edme b a za x a y tentokr\u00e1t d\u00e1me sou\u0159adnice A, abychom vypo\u010d\u00edtali a<br \/>$$5 = 10\\cdot a + 0$$<br \/>4) U\u017e v\u00edme jak\u00e9 je a a m\u016f\u017eeme napsat p\u0159epis funkce<br \/>$$a = \\frac{1}{2}$$<br \/>5) Dosad\u00edme do p\u0159episu f-ce a<br \/>$$y = ax + b$$ $$y = \\frac{1}{2}x$$<\/p>\n<p><em>b) Z\u00e1pis obecn\u00e9 rovnice p\u0159\u00edmky, kter\u00e1 je grafem funkce g<\/em><\/p>\n<p>Y [10; 0] B [x; 3] <\/p>\n<p>1) Funkce je d\u00e1na p\u0159edpisem<br \/>$$y = \\frac{1}{2}x$$<br \/>2) Za y si dosad\u00edme sou\u0159adnici B<br \/>$$3 = \\frac{1}{2}x$$<br \/>3) 3 si p\u0159evedeme na spole\u010dn\u00e9ho jmenovatele (2) a vynasob\u00edme ji s n\u00edm, t\u00edm z\u00edsk\u00e1me \u010d\u00edslo x<br \/>x = 6 \u21d2B [6; 3]<br \/>4) Z\u00edsk\u00e1me<br \/>$$\\vec{YB}= (-4; 3)$$<br \/>5) Sm\u011brov\u00fd vektor<br \/>$$\\vec{n}= (3; 4)$$<br \/>6) Obecn\u00e1 rovnice p\u0159\u00edmky<br \/>$$ax+by+c = 0$$<br \/>$$3x+4x+c=0$$<br \/>7) Dosad\u00edme do obecn\u00e9 rovnice p\u0159\u00edmky<br \/>$$3\\cdot 6 + 4\\cdot 3 + c = 0$$<br \/>8) Vypo\u010d\u00edt\u00e1me a vyjde n\u00e1m kolik je c<br \/>$$c = &#8211; 30$$<br \/>9) Nyn\u00ed to dosad\u00edme do rovnice<br \/>$$3x &#8211; 4y &#8211; 30 = 0$$<\/p>\n<p> \u010casov\u00e1 n\u00e1ro\u010dnost: 9-11 minut <\/p>\n<p>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4692","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Funkce - p\u0159\u00edklad 4 | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/funkce-priklad-4\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Funkce - p\u0159\u00edklad 4 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Grafy funkc\u00ed f a g jsou p\u0159\u00edmky. 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