Question

Which of the following functions is graphed below

Answer 1

Option C. is the correct option.

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) =
`x^(2)+4`

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.

Answer 2

Calculate the function values for x = 2

`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)`

Look at the picture.

Answer:

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