Las funciones exponenciales son las funciones que tienen la variable independiente x en el exponente.[br][br][img width=334,height=34]http://calculo.cc/temas/temas_bachillerato/primero_ciencias_sociales/funciones_elementales/imagenes/teoria/f_exponenciales/definicion.gif[/img][br][br]Las características generales de las funciones exponenciales son:[br][br]1) El dominio de una función exponencial es R.[br]2) Su recorrido es (0, +∞) .[br]3) Son funciones continuas.[br]4) Como a0 = 1 , la función siempre pasa por el punto (0, 1).[br] La función corta el eje Y en el punto (0, 1) y no corta el eje X.[br]5) Como a1 = a , la función siempre pasa por el punto (1, a).[br]6) Si a > 1 la función es creciente.[br] Si 0 < a < 1 la función es decreciente.[br]7) Son siempre concavas.[br]8) El eje X es una asíntota horizontal.[br][br]Gráfica de la Función Exponencial:[br][br][img]data:image/jpeg;base64,/9j/4AAQSkZJRgABAQAAAQABAAD/2wCEAAkGBxITDw8PEBAQDQ8OEBAODxAPDxAQDw8QFREWFhUVExMYHiggJCYlGxUVIT0iMTUrLi4uFx81ODMtNygtLisBCgoKDg0OGhAQGy4lHSUtLS0tLTAtMS4uLS0tLS0yLS0tLS0vLi0tLS0tKy0tLS0tLS0tLS0tLS0tLystLS0tLf/AABEIAKwBJAMBEQACEQEDEQH/xAAbAAEAAgMBAQAAAAAAAAAAAAAAAQUDBAYCB//EAEIQAAICAQEEBAsGBAQHAQAAAAABAgMEEQUSITEGE0FRFBUiMlRhcXSSs9MjNEKBkaEkM4LBUlNicmNzk6KyxNFE/8QAGQEBAAMBAQAAAAAAAAAAAAAAAAECAwQF/8QANREBAAIBAgQDBgQEBwAAAAAAAAECAwQREiExQRMyUSJhcZGh0RQjQlIVM4HwJEOCorHB4f/aAAwDAQACEQMRAD8A+4gAAAAAAAAAAAAAAAKXb207MeVclDrKrYypjFJ7/hT/AJKb7pcY69j0IGTHrlHJq33rZPFsdzjvKE5xnStVBt6c5fqShbBIAAAAAAAAAMDmumF85LHwqpONuZbGMpQbUq8eHlWzTXHlw9sjLLPSI7u7RUr7WW/SsfXs6OqOkUlySSXaauKZ3nd6CAAAAAAAAAAAAAAAAAAAAAAAAAAa+ZiRsUVJtblldq3Wl5UJKS19XADXs++Ve73/ADKQLAAAAAAAAABAENg2ct0cXhOZlbQa8iGuDia/5cJa2TX+6fb3QRjTnfielqvycVcHfzT/AF6R/R1SNnmpAAAAAAAAAAAAAAAAAAAAAAAAAAABWOzXNhHSS3ce7i4tRetlPmvtAswAAAAAAAAEMDnumWdKFMcel6ZGbNY1PfFy86f9MdWZ5J5bers0OKJvOS3lrzn7LbZeBGiiqitaQqhGC7+C4tv18y9Y4Y2c+XJOTJN7d24iWYAAAAAAAAAAAAAAAAAAAAAAAAAAACvmv4yr3fI+ZSBYAAAAAAAAAIkR05jlNhfxebdnvjRRvYmGux6S0ut/OS3V6o+syp7Vt+z0tR+RhrhjrPO3/UOsNnmgAAAAAAAAAAAAAAAAAAAAAAAAAAAAFfZ98q92v+ZSBYAAAAAAAAQwOc6X503GvBx5aZOa5QUlx6mladba/YnovW0ZZLfpju7tHjjnlv5a/We0LrZuFCmqumuKjXVFQil2JGlY2jZyZck5Lze3dtEqAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFX1bWdB78pKWPdpBqG7DSynXdaSfH1t+rQC0AAAAAAAA1s7LhVXZbZJQrri5zk+SSItaKxvK1MdslorXrKh6JYc7JW7Rvi4W5aiqa5c8fGXmR9r85+31GeOJ6y7dZeKxGCnSOs+sumSNXAkAAAAAAAAAAAAAAAAAAAAAAAAAAAAABX2ffKvdr/mUgWAAAAAAAIbA5LOfh+X4MuODhzUsqX4b8hNOFS71Hm/yRjPtzw9oelj/wALi4589unuj1+zrImzzd90qS5agHJd+mvL1gSAAagRqA3gJAAAAAAAAAAAAAAAAAAAAAAAVfhEZZ0IRlGU68a7fipRcob1lLjvJcVro/0AtAAAAAAhglzfSXatjnDAxGvC746znzWLQ3pK2Xr7Eu1mV7fph36XBWInNl8sfWfRabI2bDGohRX5sI8W/OnJ8XKT7W3q9S0Rw1c2bLOa83t3cx0czrro5u0bZWbldmQsauN8+pUKk4OLrWifGLe89Xq+zRFKzO27p1GOtLVxxHPaN1rRkPHwI5PVTyrpVK+1V6dZbNx3pNuWnBLXRdiSS7C8zw13c0Ui+Tg96KM5Z2LK2NVlNcqlbjXzcVPrHFvegk9VuvTjyfZqiZnlutbF4WTgn15rTYub1uJj5DXG6iu1rk9ZQUtP3JZZK7XmHjxrP0TI+PD+sEcMtjaOfCmmy+17ldUJWTfdGK1YtMQVpN7cMKKnpPKy3waOLbG6zEebBdZWmq3Ldgpt+bJt8uOmj7inFvOzotp+GvHM8t9mx0Ww764WLJlZKanKMXO93RdSnJwce3zZJNvynpx5ItXpzU1FqTPsdF+WYJAAAAAAAAAAAAAAAAAAAAAAr7PvlXu2R8ykCwAAAAENgUnSPbnUKFVUevy8huGPSnzl/im+yK5tmd77codem03iTNrcqx1n++6ejexPB4TnZLrsq99Zk3PnObXKPdFckhSm3NGq1HizERyrHKIbm1p2Ki10wdtu61XBOMdZtaJtyaWi11/ItbnVhjiOON+jT6N7FWPgU4ctJ7lbjY0uE5yblN/nKTFK7ViGmfN4mWcjHVsax014tls400+RrU4p5NCjpGFra1jotE91rXTmtWiLV3jZHiRE8cdWPC2DPHxHiUWzmpb1cbLXH+HqevCEYpJ6avTt1a1eiEV2jZa+fxL8cwvcbGjCqFUVpCEFWo81upaJfoXYTO87tZ7HxvRqP+jX/wDAcUvG3NlRyca7Fm5RhdDccoab0e5rXhwehW9d1seScd+JX7N6MqrJ8K8IyLbJU10WKbr3bdxvdlLSK05vyVpH1CK7Tu1yai1qcO0bOgiiznegAAAAAAAAAAAAAAAAAAAAAAFfZ98q92v+ZSBYAAAEagUnSDb0aNyquHhGXdqqKIvjL/VN/hiteLM737Q69Pppyb2tyrHWft73no9sN1SlkZE+vzb19rbp5MY9lda7Ir9+YpXvKdVqeOIx4+VI6e/3z717oaOLY0CeYkAAaASAYEaANACAkAAAAAAAAAAAAAAAAAAAAAABWeV4bDXd3fB7tzTXe/mU67wFmAAagcztbpDN2SxMCKyMrlOT1ePi+u6S7f8ASuLMrX7R1d+DS1iPFzTtX07z8Pu3NgbBjj71kpPIybeN2RZpvzfcu6K7Eia0iOc9WWo1U5fZjlWOkLhI0cvPu9AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAr7PvlXu1/zKQN9kDR2ptanHrdl9ka4rvfGT7orm36kRa8V6tcWHJlnasKDfy87VR6zZ2E/xNbuZevUvwJr+r2Gft390O7bDpefK1/8AbH3dBsrZdWPWq6YRriuPDnJvnKT5tvvNK1iscnDlzXyzvaW6i27JIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQwGoREqPbO1acfIqtyLYUwWPfxm9NftKeCXNlbXivVtiwZMs7UjdovbOZlcMKjqKX/APry4uP510ec/wA9DKbTbyuyMGDD/OtvP7Y+7a2V0XqhYr75Tzcr/Pv0bi/+HBeTH8i1cW3OerPLrLWjhpHDX0h0G6axycSQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEajmGoDUBvA2aO0Ns49C3r76qUv8c4r9is3iOrbHp8uTy1mVRPpdGzycPFyc19ko1uqn2uyzRaezUznLHaHTGgmvPLaK/Wfox+CbSyP5t1Wzq3zrx1117X/ADJcF+SG15T4mlxeWJtPv5R9DZ3RfGozYTUHbbZTbZO6+TtsnOM6knrLlom1w0LVxVhll12a8cO+0ekcnUbppDkSkDokAAAAAAAAAAAAAAAAAAAAAAAAAAIbA8Suiucor2tIbrcNp6Q1MnbGPXxsyKa13ythFfuyvFHdeuny26Vn5K6fTPAXBZdNj7qpda/+zUpOSnq3jQaif0sE+mdOv2WPm5L7Opw7Wn/VJJfuPFr23X/h9489qx8ZT49zJ/ytmWx7nk3VV/tFyYi957E6bDXzZIn4f+vLr2tY+M8LDj2qEbciz9Xur9mPzJTvoqdOK3x2gfRWdj1yc/LuXbCuccev2fZpP9yPDmesn42tP5eOI+PP/lu7P6K4dLUq8evfX47F1k/ilqy0Yqx2Y5Ndnvym07e7lHyhcqK7tC8fBy77jRO5z7NKz75V7tf8ykDfAAAAAAAAAAAAAAAAAAAAAAAAOW2t4w6+fUSmqfJ3N2jEn+Fa+VZdF89exf3KWraekuvFk09a/mUmZ+OzTePtJ87ctf7aNnf3vK8F/wBzT8Tp+2L6ywTws1zjCWRtVOUZSXVw2VGOkXFPj1j/AMS/ceHb9x+Lwx/lR85e1sO9+fbtufsytn1/+FiY8Kf3Sn8fEdMdflu9Po7F+fTti3/ftGp/+wPBj1n5n8Rydq1j/TCKOj+LJa+LMya1lH7W/Hk9YycXwd/eh4Ve6n8Qz9p2+ENzH2Liw03di6Ncm69nSl+rt1HhU9Fba7U263n5t5ZarcIrZt8d+ThHcWDomoSlx0u4cIvj7O8vFYhzzkvbrMy3FtGz0LJ+PC+sWUPGVnoWV8eF9YDHXtibc0sHL1rkoS1lhpauEZcPtuPCSAyeMrfQsr48L6wHi/a9kYuTwcrSK1eksNv9OuA9+MrfQsr48L6wDxlb6FlfHhfWA0bNoWeFVPwPJ18HvWm/h6v7Snj/ADgN7xlb6FlfHhfWAeMrfQsr48L6wGPH2xOcIWRwcvdnGM1vSw4vRrVap3arnyAyeMrfQsr48L6wHie17FKMXg5Ws9UvKw9OC14vrgPfjK30LK+PC+sA8ZW+hZXx4X1gPFe17JOSWDleRLcessNcdE+H23rQHvxlb6FlfHhfWAx37YnBJvBy9HKEOEsNvWc1FcFd3yXsQGTxlb6FlfHhfWAeMrfQsr48L6wGOO2JucoeA5e9GMJvysPTSTklo+u0/A/27wMnjK30LK+PC+sBEtqWJN+BZXDj5+F9YCKtq2SjGSwsrSSUlrLDT0a15dcB68ZW+hZXx4X1gMctsTU41+A5e9KM5rysPTSLinq+u0/GuHt7gMnjK30LK+PC+sA8ZWehZXx4X1gM+z83rYObqso0nZXuW7m/rCbg35EpLTVPTiBtKIDQBugNAGgDdAaAGgJAARoBIEaASAAr7PvlXu+R8ykCwAAQkBIEaASAAjQCQI0AkABCQEgQ0BKQ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