Función Irracional | Mathematics

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Función Irracional

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11th grade

Mathematics

2 hours ago by

Claudia Osuna

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Slide 1
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Función Irracional
ACADEMIA DE CÁLCULO DIFERENCIAL
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Slide 2
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Función irracional
Las funciones con radicales son las funciones que tienen la variable independiente X bajo el signo radical, es decir:
$f\left(x\right)=^n\sqrt{g\left(x\right)}$
Si n es un número par su dominio es el intervalo en el que g(x) ≥ 0 .
Si n es impar, su dominio es R (conjunto de numeros reales)
Su representación gráfica es una rama de una parábola.
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Ejemplos:
$f\left(x\right)=\sqrt{x+3}$
$f\left(x\right)=\sqrt{x^2+4}$
$f\left(x\right)=^3\sqrt{x^3+8}$
REVICEMOS EL SIGUIENTE VIDEO:
https://www.youtube.com/watch?v=CglQ0SGURAQ
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Slide 4
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TIPOS DE FUNCIONES IRRACIONALES
Cuando n es par
$f\left(x\right)=\sqrt{x+2}$
El dominio es x + 2 >= 0
resolviendo la desigualdad tenemos que x >= -2
El rango lo localizas sustituyendo x = -2 en la función original
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Slide 5
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Slide 6
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Question 7
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Q.
1. ¿Una función irracional es aquella donde la variable x esta dentro de un radical?
answer choices
Cierto
Falso
Cierto
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Falso
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Question 8
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Q.
2. ¿Una función irracional, gráficamente es una parábola?
answer choices
Cierto
Falso
Cierto
alternatives
Falso
answer explanation
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Question 9
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Q.
3. Indica cuales son funciones irracionales (son 2).
answer choices
$y\ =\ x\ +\ \sqrt{2}$
$f\left(x\right)=\sqrt{4x^2+4}$
$y=\frac{27}{\sqrt{x}}$
$f\left(x\right)=2\sqrt{5}+4x$
 <math><semantics><mrow><mi>y</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mi>x</mi><mtext> </mtext><mo>+</mo><mtext> </mtext><msqrt><mn>2</mn></msqrt></mrow><annotation encoding="application/x-tex">y\ =\ x\ +\ \sqrt{2}</annotation></semantics></math>y = x + 2<svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"></path></svg> 
alternatives
 <math><semantics><mrow><mi>f</mi><mrow><mo fence="true">(</mo><mi>x</mi><mo fence="true">)</mo></mrow><mo>=</mo><msqrt><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></msqrt></mrow><annotation encoding="application/x-tex">f\left(x\right)=\sqrt{4x^2+4}</annotation></semantics></math>f(x)=4x2+4<svg width="400em" height="1.28em" viewBox="0 0 400000 1296" preserveAspectRatio="xMinYMin slice"><path d="M263,681c0.7,0,18,39.7,52,119c34,79.3,68.167, 158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067 c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84, 175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71 c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3, -252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26 s76,-59,76,-59s76,-60,76,-60z M1001 80H40000v40H1012z"></path></svg> 
 <math><semantics><mrow><mi>y</mi><mo>=</mo><mfrac><mn>27</mn><msqrt><mi>x</mi></msqrt></mfrac></mrow><annotation encoding="application/x-tex">y=\frac{27}{\sqrt{x}}</annotation></semantics></math>y=x<svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"></path></svg>27 
 <math><semantics><mrow><mi>f</mi><mrow><mo fence="true">(</mo><mi>x</mi><mo fence="true">)</mo></mrow><mo>=</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>4</mn><mi>x</mi></mrow><annotation encoding="application/x-tex">f\left(x\right)=2\sqrt{5}+4x</annotation></semantics></math>f(x)=25<svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"></path></svg>+4x 
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Question 10
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Q.
4. Indica el dominio de la función:
$f\left(x\right)=3\sqrt{x-1}$
answer choices
$\left(\lceil1,\infty\ \right)$
$\left(\lceil-1,\ \infty\right)$
$\left(-\infty,\ 1\right)$
Ninguna
 <math><semantics><mrow><mo fence="true">(</mo><mo stretchy="false">⌈</mo><mn>1</mn><mo separator="true">,</mo><mi mathvariant="normal">∞</mi><mtext> </mtext><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\lceil1,\infty\ \right)</annotation></semantics></math>(⌈1,∞ ) 
alternatives
 <math><semantics><mrow><mo fence="true">(</mo><mo stretchy="false">⌈</mo><mo>−</mo><mn>1</mn><mo separator="true">,</mo><mtext> </mtext><mi mathvariant="normal">∞</mi><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\lceil-1,\ \infty\right)</annotation></semantics></math>(⌈−1, ∞) 
 <math><semantics><mrow><mo fence="true">(</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo separator="true">,</mo><mtext> </mtext><mn>1</mn><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(-\infty,\ 1\right)</annotation></semantics></math>(−∞, 1) 
Ninguna
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Question 12
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Q.
5. ¿Cuál seria el dominio de una raíz cubica o impar?
answer choices
(0, 0)
$\left(0,\infty\right)$
$\left(-\infty,\ 0\right)$
$\left(-\infty,\ +\infty\right)$
(0, 0)
alternatives
 <math><semantics><mrow><mo fence="true">(</mo><mn>0</mn><mo separator="true">,</mo><mi mathvariant="normal">∞</mi><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(0,\infty\right)</annotation></semantics></math>(0,∞) 
 <math><semantics><mrow><mo fence="true">(</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo separator="true">,</mo><mtext> </mtext><mn>0</mn><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(-\infty,\ 0\right)</annotation></semantics></math>(−∞, 0) 
 <math><semantics><mrow><mo fence="true">(</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo separator="true">,</mo><mtext> </mtext><mo>+</mo><mi mathvariant="normal">∞</mi><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(-\infty,\ +\infty\right)</annotation></semantics></math>(−∞, +∞) 
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