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Programa del Curso Claudio Rivera Facultad de Matemática 7 de marzo de 2013 Gráfica de Funciones Gráfica de Funciones Gráfica de Funciones Gráfica de Funciones Gráfica de Funciones Gráfica de Funciones Reflexión x y y = f(x) y = f(−x) Reflexión x y y = f(x) y = f(−x) Reflexión −a a x y y = f(x) y = f(−x) Reflexión −a a x y y = f(x) y = f(−x) Reflexión x y y = f(x) y = −f(x) Reflexión x y y = f(x) y = −f(x) Reflexión a x y y = f(x) y = −f(x) Reflexión a x y y = f(x) y = −f(x) Desplazamiento Vertical Desplazamiento Horizontal Elongamiento o Compresión Elongamiento o Compresión 0.0: 0.1: 0.2: 0.3: 0.4: 0.5: 0.6: 0.7: 0.8: 0.9: 0.10: 0.11: 0.12: 0.13: 0.14: 0.15: 0.16: 0.17: 0.18: 0.19: 0.20: 0.21: 0.22: 0.23: 0.24: 0.25: 0.26: 0.27: 0.28: 0.29: 0.30: 0.31: 0.32: 0.33: 0.34: 0.35: 0.36: 0.37: 0.38: 0.39: 0.40: 0.41: 0.42: 0.43: 0.44: 0.45: 0.46: 0.47: 0.48: 0.49: 0.50: 0.51: 0.52: 0.53: 0.54: 0.55: 0.56: 0.57: 0.58: 0.59: 0.60: 0.61: 0.62: 0.63: 0.64: 0.65: 0.66: 0.67: 0.68: 0.69: 0.70: 0.71: 0.72: 0.73: 0.74: 0.75: 0.76: 0.77: 0.78: 0.79: 0.80: 0.81: 0.82: 0.83: 0.84: 0.85: 0.86: 0.87: 0.88: 0.89: 0.90: 0.91: 0.92: 0.93: 0.94: 0.95: 0.96: 0.97: 0.98: 0.99: 0.100: 0.101: 0.102: 0.103: 0.104: 0.105: 0.106: 0.107: 0.108: 0.109: 0.110: 0.111: 0.112: 0.113: 0.114: 0.115: 0.116: 0.117: 0.118: 0.119: 0.120: 0.121: 0.122: 0.123: 0.124: 0.125: 0.126: 0.127: 0.128: 0.129: 0.130: 0.131: 0.132: 0.133: 0.134: anm0: 1.0: 1.1: 1.2: 1.3: 1.4: 1.5: 1.6: 1.7: 1.8: 1.9: 1.10: 1.11: 1.12: 1.13: 1.14: 1.15: 1.16: 1.17: 1.18: 1.19: 1.20: 1.21: 1.22: 1.23: 1.24: 1.25: 1.26: 1.27: 1.28: 1.29: 1.30: 1.31: 1.32: 1.33: 1.34: 1.35: 1.36: 1.37: 1.38: 1.39: 1.40: 1.41: 1.42: 1.43: 1.44: 1.45: 1.46: 1.47: 1.48: 1.49: 1.50: 1.51: 1.52: 1.53: 1.54: 1.55: 1.56: 1.57: 1.58: 1.59: 1.60: 1.61: 1.62: 1.63: 1.64: 1.65: 1.66: 1.67: 1.68: 1.69: 1.70: 1.71: 1.72: 1.73: 1.74: 1.75: 1.76: 1.77: 1.78: 1.79: 1.80: 1.81: 1.82: 1.83: 1.84: 1.85: 1.86: 1.87: 1.88: 1.89: 1.90: 1.91: 1.92: 1.93: 1.94: 1.95: 1.96: 1.97: 1.98: 1.99: 1.100: 1.101: 1.102: 1.103: 1.104: 1.105: 1.106: 1.107: 1.108: 1.109: 1.110: 1.111: 1.112: 1.113: 1.114: 1.115: 1.116: 1.117: 1.118: 1.119: 1.120: 1.121: 1.122: 1.123: 1.124: 1.125: 1.126: 1.127: 1.128: 1.129: 1.130: 1.131: 1.132: 1.133: 1.134: anm1: 2.0: 2.1: 2.2: 2.3: 2.4: 2.5: 2.6: 2.7: 2.8: 2.9: 2.10: 2.11: 2.12: 2.13: 2.14: 2.15: 2.16: 2.17: 2.18: 2.19: 2.20: 2.21: 2.22: 2.23: 2.24: 2.25: 2.26: 2.27: 2.28: 2.29: 2.30: 2.31: 2.32: 2.33: 2.34: 2.35: 2.36: 2.37: 2.38: 2.39: 2.40: 2.41: 2.42: 2.43: 2.44: 2.45: 2.46: 2.47: 2.48: 2.49: 2.50: 2.51: 2.52: 2.53: 2.54: 2.55: 2.56: 2.57: 2.58: 2.59: 2.60: 2.61: 2.62: 2.63: 2.64: 2.65: 2.66: 2.67: 2.68: 2.69: 2.70: 2.71: 2.72: 2.73: 2.74: 2.75: 2.76: 2.77: 2.78: 2.79: 2.80: 2.81: 2.82: 2.83: 2.84: 2.85: 2.86: 2.87: 2.88: 2.89: 2.90: 2.91: 2.92: 2.93: 2.94: 2.95: 2.96: 2.97: 2.98: 2.99: 2.100: 2.101: 2.102: 2.103: 2.104: 2.105: 2.106: 2.107: anm2: 3.0: 3.1: 3.2: 3.3: 3.4: 3.5: 3.6: 3.7: 3.8: 3.9: 3.10: 3.11: 3.12: 3.13: 3.14: 3.15: 3.16: 3.17: 3.18: 3.19: 3.20: 3.21: 3.22: 3.23: 3.24: 3.25: 3.26: 3.27: 3.28: 3.29: 3.30: 3.31: 3.32: 3.33: 3.34: 3.35: 3.36: 3.37: 3.38: 3.39: 3.40: 3.41: 3.42: 3.43: 3.44: 3.45: 3.46: 3.47: 3.48: 3.49: 3.50: 3.51: 3.52: 3.53: 3.54: 3.55: 3.56: 3.57: 3.58: 3.59: 3.60: 3.61: 3.62: 3.63: 3.64: 3.65: 3.66: 3.67: 3.68: 3.69: 3.70: 3.71: 3.72: 3.73: 3.74: 3.75: 3.76: 3.77: 3.78: 3.79: 3.80: 3.81: 3.82: 3.83: 3.84: 3.85: 3.86: 3.87: 3.88: 3.89: 3.90: 3.91: 3.92: 3.93: 3.94: 3.95: 3.96: 3.97: 3.98: 3.99: 3.100: 3.101: 3.102: 3.103: 3.104: 3.105: 3.106: 3.107: 3.108: 3.109: 3.110: 3.111: 3.112: 3.113: 3.114: 3.115: 3.116: 3.117: 3.118: 3.119: 3.120: 3.121: 3.122: 3.123: 3.124: 3.125: 3.126: 3.127: 3.128: 3.129: 3.130: 3.131: 3.132: 3.133: 3.134: 3.135: 3.136: 3.137: 3.138: 3.139: 3.140: 3.141: 3.142: 3.143: 3.144: 3.145: 3.146: 3.147: 3.148: 3.149: 3.150: anm3: 4.0: 4.1: 4.2: 4.3: 4.4: 4.5: 4.6: 4.7: 4.8: 4.9: 4.10: 4.11: 4.12: 4.13: 4.14: 4.15: 4.16: 4.17: 4.18: 4.19: 4.20: 4.21: 4.22: 4.23: 4.24: 4.25: 4.26: 4.27: 4.28: 4.29: 4.30: 4.31: 4.32: 4.33: 4.34: 4.35: 4.36: 4.37: 4.38: 4.39: 4.40: 4.41: 4.42: 4.43: 4.44: 4.45: 4.46: 4.47: 4.48: 4.49: 4.50: 4.51: 4.52: 4.53: 4.54: 4.55: 4.56: 4.57: 4.58: 4.59: 4.60: 4.61: 4.62: 4.63: 4.64: 4.65: 4.66: 4.67: 4.68: 4.69: 4.70: 4.71: 4.72: 4.73: 4.74: 4.75: 4.76: 4.77: 4.78: 4.79: 4.80: 4.81: 4.82: 4.83: 4.84: 4.85: 4.86: 4.87: 4.88: 4.89: 4.90: 4.91: 4.92: 4.93: 4.94: 4.95: 4.96: 4.97: 4.98: 4.99: 4.100: 4.101: 4.102: 4.103: 4.104: 4.105: 4.106: 4.107: 4.108: 4.109: 4.110: 4.111: 4.112: 4.113: 4.114: 4.115: 4.116: 4.117: 4.118: 4.119: 4.120: 4.121: 4.122: 4.123: 4.124: 4.125: 4.126: 4.127: 4.128: 4.129: 4.130: anm4: 5.0: 5.1: 5.2: 5.3: 5.4: 5.5: 5.6: 5.7: 5.8: 5.9: 5.10: 5.11: 5.12: 5.13: 5.14: 5.15: 5.16: 5.17: 5.18: 5.19: 5.20: 5.21: 5.22: 5.23: 5.24: 5.25: 5.26: 5.27: 5.28: 5.29: 5.30: 5.31: 5.32: 5.33: 5.34: 5.35: 5.36: 5.37: 5.38: 5.39: 5.40: 5.41: 5.42: 5.43: 5.44: 5.45: 5.46: 5.47: 5.48: 5.49: 5.50: 5.51: 5.52: 5.53: 5.54: 5.55: 5.56: 5.57: 5.58: 5.59: 5.60: 5.61: 5.62: 5.63: 5.64: 5.65: 5.66: 5.67: 5.68: 5.69: 5.70: 5.71: 5.72: 5.73: 5.74: 5.75: 5.76: 5.77: 5.78: 5.79: 5.80: 5.81: 5.82: 5.83: 5.84: 5.85: 5.86: 5.87: 5.88: 5.89: 5.90: 5.91: 5.92: 5.93: 5.94: 5.95: 5.96: 5.97: 5.98: 5.99: 5.100: 5.101: 5.102: 5.103: 5.104: 5.105: 5.106: 5.107: 5.108: 5.109: 5.110: 5.111: 5.112: 5.113: 5.114: 5.115: 5.116: 5.117: 5.118: 5.119: 5.120: 5.121: 5.122: 5.123: 5.124: 5.125: 5.126: 5.127: 5.128: 5.129: 5.130: anm5: 6.0: 6.1: 6.2: 6.3: 6.4: 6.5: 6.6: 6.7: 6.8: 6.9: 6.10: 6.11: 6.12: 6.13: 6.14: 6.15: 6.16: 6.17: 6.18: 6.19: 6.20: 6.21: 6.22: 6.23: 6.24: 6.25: 6.26: 6.27: 6.28: 6.29: 6.30: 6.31: 6.32: 6.33: 6.34: 6.35: 6.36: 6.37: 6.38: 6.39: 6.40: 6.41: 6.42: 6.43: 6.44: 6.45: 6.46: 6.47: 6.48: 6.49: 6.50: 6.51: 6.52: 6.53: 6.54: 6.55: 6.56: 6.57: 6.58: 6.59: 6.60: 6.61: 6.62: 6.63: 6.64: 6.65: 6.66: 6.67: 6.68: 6.69: 6.70: 6.71: 6.72: 6.73: 6.74: 6.75: 6.76: 6.77: 6.78: 6.79: 6.80: 6.81: 6.82: 6.83: 6.84: 6.85: 6.86: 6.87: 6.88: 6.89: 6.90: 6.91: 6.92: 6.93: 6.94: 6.95: 6.96: 6.97: 6.98: 6.99: 6.100: 6.101: 6.102: 6.103: 6.104: 6.105: 6.106: 6.107:6.108: 6.109: 6.110: 6.111: 6.112: 6.113: 6.114: 6.115: 6.116: 6.117: 6.118: 6.119: 6.120: 6.121: 6.122: 6.123: 6.124: 6.125: 6.126: 6.127: 6.128: 6.129: 6.130: 6.131: 6.132: 6.133: 6.134: 6.135: 6.136: 6.137: 6.138: 6.139: 6.140: 6.141: 6.142: 6.143: 6.144: 6.145: 6.146: 6.147: 6.148: 6.149: 6.150: anm6: 7.0: 7.1: 7.2: 7.3: 7.4: 7.5: 7.6: 7.7: 7.8: 7.9: 7.10: 7.11: 7.12: 7.13: 7.14: 7.15: 7.16: 7.17: 7.18: 7.19: 7.20: 7.21: 7.22: 7.23: 7.24: 7.25: 7.26: 7.27: 7.28: 7.29: 7.30: 7.31: 7.32: 7.33: 7.34: 7.35: 7.36: 7.37: 7.38: 7.39: 7.40: 7.41: 7.42: 7.43: 7.44: 7.45: 7.46: 7.47: 7.48: 7.49: 7.50: 7.51: 7.52: 7.53: 7.54: 7.55: 7.56: 7.57: 7.58: 7.59: 7.60: 7.61: 7.62: 7.63: 7.64: 7.65: 7.66: 7.67: 7.68: 7.69: 7.70: 7.71: 7.72: 7.73: 7.74: 7.75: 7.76: 7.77: 7.78: 7.79: 7.80: 7.81: 7.82: 7.83: 7.84: 7.85: 7.86: 7.87: 7.88: 7.89: 7.90: 7.91: 7.92: 7.93: 7.94: 7.95: 7.96: 7.97: 7.98: 7.99: 7.100: 7.101: 7.102: 7.103: 7.104: 7.105: 7.106: 7.107: 7.108: 7.109: 7.110: 7.111: 7.112: 7.113: 7.114: 7.115: 7.116: 7.117: 7.118: 7.119: 7.120: 7.121: 7.122: 7.123: 7.124: 7.125: 7.126: 7.127: 7.128: 7.129: 7.130: 7.131: 7.132: 7.133: 7.134: 7.135: 7.136: 7.137: 7.138: 7.139: 7.140: 7.141: 7.142: 7.143: 7.144: 7.145: 7.146: 7.147: 7.148: 7.149: 7.150: 7.151: 7.152: 7.153: 7.154: 7.155: 7.156: 7.157: 7.158: 7.159: 7.160: 7.161: 7.162: 7.163: 7.164: 7.165: 7.166: 7.167: 7.168: 7.169: 7.170: 7.171: 7.172: 7.173: 7.174: 7.175: 7.176: 7.177: 7.178: 7.179: 7.180: 7.181: 7.182: 7.183: 7.184: 7.185: 7.186: 7.187: 7.188: 7.189: 7.190: 7.191: 7.192: 7.193: 7.194: 7.195: 7.196: 7.197: 7.198: 7.199: 7.200: anm7: 8.0: 8.1: 8.2: 8.3: 8.4: 8.5: 8.6: 8.7: 8.8: 8.9: 8.10: 8.11: 8.12: 8.13: 8.14: 8.15: 8.16: 8.17: 8.18: 8.19: 8.20: 8.21: 8.22: 8.23: 8.24: 8.25: 8.26: 8.27: 8.28: 8.29: 8.30: 8.31: 8.32: 8.33: 8.34: 8.35: 8.36: 8.37: 8.38: 8.39: 8.40: 8.41: 8.42: 8.43: 8.44: 8.45: 8.46: 8.47: 8.48: 8.49: 8.50: 8.51: 8.52: 8.53: 8.54: 8.55: 8.56: 8.57: 8.58: 8.59: 8.60: 8.61: 8.62: 8.63: 8.64: 8.65: 8.66: 8.67: 8.68: 8.69: 8.70: 8.71: 8.72: 8.73: 8.74: 8.75: 8.76: 8.77: 8.78: 8.79: 8.80: 8.81: 8.82: 8.83: 8.84: 8.85: 8.86: 8.87: 8.88: 8.89: 8.90: 8.91: 8.92: 8.93: 8.94: 8.95: 8.96: 8.97: 8.98: 8.99: 8.100: 8.101: 8.102: 8.103: 8.104: 8.105: 8.106: 8.107: 8.108: 8.109: 8.110: 8.111: 8.112: 8.113: 8.114: 8.115: 8.116: 8.117: 8.118: 8.119: 8.120: 8.121: 8.122: 8.123: 8.124: 8.125: 8.126: 8.127: 8.128: 8.129: 8.130: 8.131: 8.132: 8.133: 8.134: 8.135: 8.136: 8.137: 8.138: 8.139: 8.140: 8.141: 8.142: 8.143: 8.144: 8.145: 8.146: 8.147: 8.148: 8.149: 8.150: 8.151: 8.152: 8.153: 8.154: 8.155: 8.156: 8.157: 8.158: 8.159: 8.160: 8.161: 8.162: 8.163: 8.164: 8.165: 8.166: 8.167: 8.168: 8.169: 8.170: 8.171: 8.172: 8.173: 8.174: 8.175: 8.176: 8.177: 8.178: 8.179: 8.180: 8.181: 8.182: 8.183: 8.184: 8.185: 8.186: 8.187: 8.188: 8.189: 8.190: 8.191: 8.192: 8.193: 8.194: 8.195: 8.196: 8.197: 8.198: 8.199: 8.200: anm8: 9.0: 9.1: 9.2: 9.3: 9.4: 9.5: 9.6: 9.7: 9.8: 9.9: 9.10: 9.11: 9.12: 9.13: 9.14: 9.15: 9.16: 9.17: 9.18: 9.19: 9.20: 9.21: 9.22: 9.23: 9.24: 9.25: 9.26: 9.27: 9.28: 9.29: 9.30: 9.31: 9.32: 9.33: 9.34: 9.35: 9.36: 9.37: 9.38: 9.39: 9.40: 9.41: 9.42: 9.43: 9.44: 9.45: 9.46: 9.47: 9.48: 9.49: 9.50: 9.51: 9.52: 9.53: 9.54: 9.55: 9.56: 9.57: 9.58: 9.59: 9.60: 9.61: 9.62: 9.63: 9.64: 9.65: 9.66: 9.67: 9.68: 9.69: 9.70: 9.71: 9.72: 9.73: 9.74: 9.75: 9.76: 9.77: 9.78: 9.79: 9.80: 9.81: 9.82: 9.83: 9.84: 9.85: 9.86: 9.87: 9.88: 9.89: 9.90: 9.91: 9.92: 9.93: 9.94: 9.95: 9.96: 9.97: 9.98: 9.99: 9.100: 9.101: 9.102: 9.103: 9.104: 9.105: 9.106: 9.107: 9.108: 9.109: 9.110: 9.111: 9.112: 9.113: 9.114: 9.115: 9.116: 9.117: 9.118: 9.119: 9.120: 9.121: 9.122: 9.123: 9.124: 9.125: 9.126: 9.127: 9.128: 9.129: 9.130: 9.131: 9.132: 9.133: 9.134: 9.135: 9.136: 9.137: 9.138: 9.139: 9.140: 9.141: 9.142: 9.143: 9.144: 9.145: 9.146: 9.147: 9.148: 9.149: 9.150: 9.151: 9.152: 9.153: 9.154: 9.155: 9.156: 9.157: 9.158: 9.159: 9.160: 9.161: 9.162: 9.163: 9.164: 9.165: 9.166: 9.167: 9.168: 9.169: 9.170: 9.171: 9.172: 9.173: 9.174: 9.175: 9.176: 9.177: 9.178: 9.179: 9.180: 9.181: 9.182: 9.183: 9.184: 9.185: 9.186: 9.187: 9.188: 9.189: 9.190: 9.191: 9.192: 9.193: 9.194: 9.195: 9.196: 9.197: anm9:
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