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Which of the given functions could this graph represent?

A. f(x) = x(x − 1)(x + 1)
B. f(x) = (x − 1)(x − 2)(x + 1)(x + 2)
C. f(x) = x(x − 1)(x − 2)(x + 1)(x + 2)
D. f(x) = x(x − 1)(x − 2)

Which of the given functions could this graph represent A fx xx 1x 1 B fx x 1x 2x 1x 2 C fx xx 1x 2x 1x 2 D fx xx 1x 2 class=

Respuesta :

Answer:

B. f(x) = (x − 1)(x − 2)(x + 1)(x + 2)

Step-by-step explanation:

Choice A will be a transformation of the function f(x) = x³.  The parent function goes from the third quadrant through the origin into the first quadrant.  This is not a cubic function.

Choice C will be a transformation of the function f(x) = x⁵.  The parent function goes from the third quadrant through the origin into the first quadrant.  This is not one of those functions.

Choice D will be a transformation of the function f(x) = x³.  This is not a cubic function.

Choice D will be a transformation of the function f(x) = x⁴.  These functions go from the second quadrant across the y-axis into the first quadrant.  This is a quartic function.

The function which represent the graph shown in the image is f(x)=(x − 1)(x − 2)(x + 1)(x + 2). Option B is correct.

Which is the graph of function?

A graph of function is the way of representation of a function visually on the x-y coordinate system.

A graph is shown in the image. The vertex point of the graph are (0,4) and x intersects are (-2,0),(1,0),(-1,0) and (2,0). Thus, the equation from these vertices can be given as,

f(x) = x(x − 1)(x − 2)(x + 1)(x + 2)

The graph with vertex and intersection point is attached below. Thus, the function which represent the graph shown in the image is f(x)=(x − 1)(x − 2)(x + 1)(x + 2). Option B is correct.

Learn more about the graph of a function here;

https://brainly.com/question/62792

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