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Suppose f(x) = x2 and g(x) = . Which statement best compares the graph of g(x) with the graph of f(x)?A.The graph of g(x) is horizontally stretched by a factor of 4.B.The graph of g(x) is shifted 4 units to the right.C.The graph of g(x) is horizontally compressed by a factor of 4.D.The graph of g(x) is vertically compressed by a factor of 4.

Question

Suppose f(x) = x2 and g(x) = . Which statement best compares the graph of g(x) with the graph of f(x)?A.The graph of g(x) is horizontally stretched by a factor of 4.B.The graph of g(x) is shifted 4 units to the right.C.The graph of g(x) is horizontally compressed by a factor of 4.D.The graph of g(x) is vertically compressed by a factor of 4.

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Solution

Para resolver la pregunta, primero necesitamos entender las funciones dadas y cómo se relacionan entre sí.

  1. La función f(x)=x2 f(x) = x^2 es una parábola estándar con vértice en el origen (0,0) y se abre hacia arriba.

  2. La función g(x) g(x) no está completamente especificada en la pregunta, pero asumiremos que hay un error tipográfico y que debería ser g(x)=(x/4)2 g(x) = (x/4)^2 .

Ahora, comparemos g(x) g(x) con f(x) f(x) :

  • f(x)=x2 f(x) = x^2
  • g(x)=(x/4)2 g(x) = (x/4)^2

Podemos reescribir g(x) g(x) como: g(x)=(x4)2=x216 g(x) = \left(\frac{x}{4}\right)^2 = \frac{x^2}{16}

Para entender cómo se transforma la gráfica de f(x) f(x) en la gráfica de g(x) g(x) , observemos los efectos de las transformaciones:

  • La expresión (x4)2 \left(\frac{x}{4}\right)^2 indica una transformación horizontal. Dividir x x por 4 significa que cada valor de x x en f(x) f(x) se multiplica por 4 en g(x) g(x) . Esto es una compresión horizontal por un factor de 4.

Por lo tanto, la respuesta correcta es:

C. The graph of g(x) is horizontally compressed by a factor of 4.

This problem has been solved

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