CÁLCULO/2. FUNCIONES FUNCIONES.01. Dado un gráfico (de varias funciones) estimar: 1. Imagen de un valor 2. Preimagen

Dado el gráfico de la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»g«/mi»«mn»1«/mn»«mo»(«/mo»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«mo»)«/mo»«/math», determina:

#graf1

1) Imagen de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»k«/mi»«mn»3«/mn»«/math»

2) Preimagen de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»I«/mi»«mi»m«/mi»«mn»2«/mn»«/math»

Obs:

1) Si el gráfico de la función corresponde a una parábola y existen más de una preimagen, escribe tu respuesta de la forma «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»{«/mo»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«mo»=«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«mo»=«/mo»«mi»b«/mi»«mo»}«/mo»«/math», si existe una sola preimagen escribe el número como tu respuesta.

2) Si el gráfico corresponde a una función trigonométrica (por ejemplo la función coseno), escribe solo la preimagen positiva más cercana al cero como tu respuesta.

]]> 1.0000000 0.3333333 0 0 1) Imagen= #Im2) Preimagen=#Preim]]> #retropersonal

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xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mi>sig</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>h1</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>k1</mi><mo>,</mo><mn>2</mn><mo>→</mo><mi>sig</mi><mo>*</mo><msqrt><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></msqrt><mo>+</mo><mi>k1</mi><mo>,</mo><mn>3</mn><mo>→</mo><mi>k1</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>k1</mi><mo>*</mo><mi>h1</mi><mo>,</mo><mn>4</mn><mo>→</mo><mi>sig</mi><mo>*</mo><mi>a1</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mfrac><mrow><mn>2</mn><pi/></mrow><mi>b2</mi></mfrac><mo>*</mo><mi>x</mi><mo>)</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>minf2</mi><mo>=</mo><mi>min</mi><mo>(</mo><mi>f2</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>,</mo><mi>f2</mi><mo>(</mo><mi>b1</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>minf3</mi><mo>=</mo><mi>min</mi><mo>(</mo><mi>f3</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>,</mo><mi>f3</mi><mo>(</mo><mi>b1</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>minf4</mi><mo>=</mo><mo>-</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>maxf1</mi><mo>*</mo><mi>minf1</mi><mo>⩾</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>cf1</mi><mo>=</mo><mi>signo</mi><mo>(</mo><mi>maxf1</mi><mo>)</mo><mo>*</mo><mi>max</mi><mo>(</mo><mfenced close="|" 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actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Definición</mi><mo> </mo><mi>de</mi><mo> </mo><mi>los</mi><mo> </mo><mi>tableros</mi><mo>:</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo> </mo><mi>Centros</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C1</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mi>punto</mi><mo>(</mo><mfrac><mrow><mi>b1</mi><mo>+</mo><mi>a1</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mi>cf1</mi><mo>)</mo><mo>,</mo><mn>2</mn><mo>→</mo><mi>punto</mi><mo>(</mo><mfrac><mrow><mi>b1</mi><mo>+</mo><mi>a1</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mi>cf2</mi><mo>)</mo><mo>,</mo><mn>3</mn><mo>→</mo><mi>punto</mi><mfenced><mrow><mfrac><mrow><mi>b1</mi><mo>+</mo><mi>a1</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mo>(</mo><mi>maxf3</mi><mo>+</mo><mi>minf3</mi><mo>)</mo><mo>/</mo><mn>2</mn></mrow></mfenced><mo>,</mo><mn>4</mn><mo>→</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>C1</mi><mo>(</mo><mi>w1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>C1</mi><mo>(</mo><mi>w1</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>C1</mi><mo>(</mo><mi>w1</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>C1</mi><mo>(</mo><mi>w1</mi><mo>+</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mo>(</mo><mi>b1</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>+</mo><mn>10</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>al3</mi><mo>=</mo><mo>(</mo><mi>maxf3</mi><mo>-</mo><mi>minf3</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>al4</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>*</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Altura</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Al</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>→</mo><mi>al1</mi><mo>,</mo><mn>2</mn><mo>→</mo><mi>al2</mi><mo>,</mo><mn>3</mn><mo>→</mo><mi>al3</mi><mo>,</mo><mn>4</mn><mo>→</mo><mi>al4</mi><mo>,</mo><mn>5</mn><mo>→</mo><mi>al1</mi><mo>,</mo><mn>6</mn><mo>→</mo><mi>al2</mi><mo>,</mo><mn>7</mn><mo>→</mo><mi>al3</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alt1</mi><mo>=</mo><mi>Al</mi><mo>(</mo><mi>w1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>centro</mi><mo>=</mo><mi>c1</mi><mo>,</mo><mi>anchura</mi><mo>=</mo><mi>an</mi><mo>,</mo><mi>altura</mi><mo>=</mo><mi>alt1</mi><mo>,</mo><mi>etiqueta_de_ejes</mi><mo>=</mo><mo>{</mo><mi>v1</mi><mo>,</mo><mi>g1</mi><mo>(</mo><mi>v1</mi><mo>)</mo><mo>}</mo><mo>,</mo><mi>altura_ventana</mi><mo>=</mo><mn>500</mn><mo>,</mo><mi>anchura_ventana</mi><mo>=</mo><mn>500</mn><mo>}</mo><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Gráfico</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf1</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>R1</mi><mo>(</mo><mi>w1</mi><mo>)</mo><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Selección</mi><mo> </mo><mi>de</mi><mo> </mo><mi>Imagen</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>k1</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><msub><mi>c1</mi><mn>1</mn></msub><mo>-</mo><mi>an</mi><mo>/</mo><mn>2</mn><mo>)</mo></mrow></mfenced><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>k2</mi><mo>=</mo><mfenced close="⌉" open="⌈"><mrow><mo>(</mo><msub><mi>c1</mi><mn>1</mn></msub><mo>+</mo><mi>an</mi><mo>/</mo><mn>2</mn><mo>)</mo></mrow></mfenced><mo>-</mo><mn>1</mn></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>alt2</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><msub><mi>c1</mi><mn>2</mn></msub><mo>-</mo><mi>alt1</mi><mo>/</mo><mn>2</mn><mo>)</mo></mrow></mfenced><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>alt3</mi><mo>=</mo><mfenced close="⌉" 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type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>)</mo><mo> </mo><mi>I</mi><mi>m</mi><mi>a</mi><mi>g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>I</mi><mi>m</mi><mspace linebreak="newline"/><mn>2</mn><mo>)</mo><mo> </mo><mi>P</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>a</mi><mi>g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo>=</mo><mo>#</mo><mi>P</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">i</mi><mi>m</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">50 50</data><data name="casSession"/></localData></question>