ࡱ> PROW[ Ibjbj Kΐΐ%  SSSSSggg8C\gx("DDD$Y z&uSD@DDD&SSDSSD0gsg0u!u!u!S DDDDDDD&&DDDDDDDu!DDDDDDDDD  : TEMA 6: FUNCIONES ELEMENTALES II. RESUELVE Y COMPRUEBA Ejercicio n 1.- Representa la funcin de ecuacin:  EMBED Equation.3  Solucin: Por ser una funcin cuadrtica, su representacin es una parbola. Hallamos su vrtice:  Puntos de corte con los ejes:    Con eje Y x = 0 y = 4 (0, 4) Puntos prximos al vrtice:  Ejercicio n 2.- Relaciona cada una de las siguientes expresiones con su grfica correspondiente: a) y = -x2 - 3x b) y = (x - 3)2 c) y = -2 - 3x2  Solucin: a) I b) IV c) II d) III Ejercicio n 3.- Completa las expresiones de estas dos grficas:    Solucin: Parbola a) Punto de corte con el eje Y: (0, 10) c = 10  Ecuacin de a): y = 3x2 + 12x + 10 Parbola b) c = 4 la ecuacin ser de la forma y = ax2 + 4. Un punto de la parbola es el (1, 1), as: 1 = a + 4 a = -3 La ecuacin buscada es: y = -3x2 + 4 Ejercicio n 4.- Representa la siguiente funcin:  Solucin: El primer trozo es la recta constante y = -4 definida para x < - 2. Representamos la recta   El ltimo tramo es un trozo de la parbola y = x2 - 4 definida para x 1:   Ejercicio n 5.- Asocia a cada grfica una de estas expresiones:  b) y = 5x c) y = log3 (x + 1)   Solucin: a) II b) III c) I d) IV Ejercicio n 6.- a) De la siguiente hiprbola, di cul es su dominio, cules son sus asintotas y represntala:   Haz la representacin grfica. Solucin: a) Dominio de definicin:  EMBED Equation.3  Tabla de valores en puntos prximos a x = 0:  Tabla de valores para otros puntos:  Se observa que los valores de y estn prximos a -3 cuando x se hace muy grande o muy pequea. Luego las asntotas son las rectas x = 0, y = -3.  b) Para que el dominio de definicin sean los valores de x 4, se necesita tomar k = 4 (as, x - 4 0). 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Hacemos una tabla de valores:   b) El dominio de definicin de y = log5 x es (0, +), luego el punto (-1, 2) no pertenece al dominio por ser x = -1 < 0. El resto de puntos tienen abscisa positiva, luego pueden pertenecer a la grfica de la funcin:    Los puntos que pertenecen a la grfica son:  Ejercicio n 8.- Se cerca una finca rectangular de rea A con 42 m de alambrada, sin que sobre ni falte nada. a) Expresa el rea de la finca en funcin de uno de sus lados b) Representa grficamente la expresin anterior. c) Cul es el dominio de definicin? d) Para qu valor de los lados obtenemos la finca de rea mxima? Solucin: Las dimensiones de la finca son x, 21 - x. a) A = rea de la finca La expresin analtica buscada es A(x) = x (21 - x) A(x) = -x2 + 21x, que es una funcin cuadrtica. b) Ser una parbola abierta hacia abajo:  V (10,5; 110,25) Puntos de corte con los ejes:  (0, 0) y (21, 0) Eje Y x = 0 y = 0 (0, 0) Tabla de valores:   c) Por ser x una longitud y A(x) un rea, la grfica corresponde solo al primer cuadrante. Dominio de definicin: (0, 21) d) El rea es mxima en el vrtice, y mide 110,25 m2. Se obtiene tomando como lados x = 10,5 m y 21-10,5 = 10,5 m es decir, el rea es mxima si la finca es cuadrada. Ejercicio n 9.- Calcula, usando la definicin de logaritmo:   c) log3 243 Solucin:    Ejercicio n 10.- Resuelve las ecuaciones siguientes:  b) log2 (x - 1) = -2 Solucin: a) Expresamos el primer miembro como potencia de 7 e igualamos exponentes:   b) Aplicando la definicin de logaritmo, se obtiene:  Comprobacin de la solucin       PAGE  PAGE 1 :(:.:0:d:f:h:j:n:v:|:~::::::::;;;;;;";$;*;,;.;B;D;ﲡﲏ}lZ#jh 0CJOJQJU^JaJ h 06CJOJQJ]^JaJ#j h 0CJOJQJU^JaJ#h 05CJH*OJQJ\^JaJ h 05CJOJQJ\^JaJ&h 056CJOJQJ\]^JaJ)h 056CJH*OJQJ\]^JaJ#h 05CJH*OJQJ\^JaJU h 05CJOJQJ\^JaJ!D;v;x;z;|;;;;;;;;;< <"<$<&<*<,<j<l<n<p<r<x<|<~<<<<<<<<<===== =$=&==h 0CJH*OJQJ^JaJ h 05CJOJQJ\^JaJ#jh 0CJOJQJU^JaJ#j<h 0CJOJQJU^JaJh 0CJH*OJQJ^JaJh 0CJOJQJ^JaJ h 06CJOJQJ]^JaJh 0CJOJQJ^JaJ,;<"<&<(<<=t======>Z>^>`>b>d>f>>F??*@$1$7$8$H$^`a$ 1$7$8$H$^1$7$8$H$ 1$7$8$H$^=====>Z>\>f>>>>H?J???,@.@z@|@@AAAXAZAhA߻ߩߔo^^^^MoM h 06CJOJQJ]^JaJ h 05CJOJQJ\^JaJ&h 056CJOJQJ\]^JaJ h 05CJOJQJ\^JaJ)h 056>*CJOJQJ\]^JaJ#jh 0CJOJQJU^JaJ#j>h 0CJOJQJU^JaJ#jĿh 0CJOJQJU^JaJh 0CJOJQJ^JaJ#jh 0CJOJQJU^JaJ*@x@AAArAAADBBBBBCFCJCpCCD DDD S1$7$8$H$^S 1$7$8$H$^ "1$7$8$H$^" 1$7$8$H$^ 1$7$8$H$^1$7$8$H$hAjAlAnAtAvAzA|A~AAAAAAAAAAAABBB B BBBBBB B"B$B&B(B*B,B.B0B2B4B:B*CJOJQJ\]^JaJh 0CJOJQJ^JaJh 0CJOJQJ^JaJh 0@CJOJQJ^JaJh 0@CJOJQJ^JaJ$h 06@CJOJQJ]^JaJGG"G4G6G8GGBGDGNGrGGGGGGGGGGGGGʼq_N*CJOJQJ\]^JaJ#jwh 0CJOJQJU^JaJ#jh 0CJOJQJU^JaJ#j h 0CJOJQJU^JaJh 0CJOJQJ^JaJ&h 056CJOJQJ\]^JaJ h 05CJOJQJ\^JaJ h 06CJOJQJ]^JaJBGFGHGJGLGNGrGGGGGGGHHHHHHIIIRITIXI\I^I`I 1$7$8$H$^1$7$8$H$GGGGGGGGGGHHHHHHHHIIITIVIXIZI`I龎ygUC#jz-h 0CJOJQJU^JaJ#jl)h 0CJOJQJU^JaJ#jN%h 0CJOJQJU^JaJh 0CJOJQJ^JaJ#j"h 0CJOJQJU^JaJ#jh 0CJOJQJU^JaJh 0CJOJQJ^JaJ&h 056CJOJQJ\]^JaJ h 06CJOJQJ]^JaJ h 05CJOJQJ\^JaJ h 05CJOJQJ\^JaJ`IbIfIhIlInIrItIxIzIIIIIIIIIh]h&`#$1$7$8$H$`IbIdIhIjInIpItIvIzI|IIIIIIIIIIIIIh# 0JmHnHu h 00Jjh 00JUh 0jh 0U"h 0CJOJQJ^JaJmH sH 50P/ =!"-#S$% Dp`! 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