Respuesta :

gmany

Calculate the function values for x = 2

[tex]y=x^2+4\\\\for\ x=2\to y=2^2+4=4+4=8\to(2,\ 8)\\\\y=-x+4\\\\for\ x=2\to y=-2+4=2\to(2,\ 2)[/tex]

Look at the picture.

Answer:

[tex]C.\ \left\{\begin{array}{ccc}x^2+4&.\ x<2\\-x+4&,\ x\geq2\end{array}\right[/tex]

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Answer:

Option C. is the correct option.

Step-by-step explanation:

There are two portions of the given graph. One is in the curved form and second is the straight line.

In the curved portion a Hollow point is given with x coordinate as 2 and the function value of f(2) =  8.

f(x) = [tex]x^{2}+4[/tex]

f(2) = 4+4 = 8

And hollow point represents x < 2.

Similarly in the second portion of the graph which is in the form of a straight line, starting point is in the solid form which represents x ≥ 2.

The function value at x ≥ 2 is 2.

f(x) = -x + 4

f(2) = -2 + 4 = 2

Therefore Option C. is the correct answer.

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