Question

Which rule describes the function in the graph below?

Answer 1

Answer is B g(x)=-1/2x+1

Answer 2

A rule that describes the piecewise-defined function in the graph above include the following: B.
`f(x)=\left\{\begin{array}{Ir}-(1)/(2) x+1, & x < -2\\-x^(2) +6 ,& -2\leq x < 0\\6 ,& 0 < x\leq 4\\x+2, & x > 4\end{array}\right`.

A piecewise-defined function is a type of function that is defined by two or more mathematical expressions over a specific domain.

Note: The inequality symbol < or > represents a hollow dot (circle).

The inequality symbol ≤ or ≥ represents a solid dot (circle).

Generally speaking, the domain of any piecewise-defined function is the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we have the following functions;

Over the interval x < -2, a downward sloping lineextends infinitely to the left and must be denoted by this function;

g(x) = -1/2(x) + 1, when x < -2.

Over the interval -2 ≤ x < 0, a curve approaches the point (0, 6) and must be denoted by this function;

g(x) =
`-x^(2) +6`, when -2 ≤ x < 0.

Over the interval 0 < x ≤ 4, a horizontal line approaches the point (4, 6) and must be denoted by this function;

g(x) = 6, when 0 < x ≤ 4.

Over the interval x > 4, a upward sloping line extends infinitely and must be denoted by this function;

g(x) = x + 2, when x > 4.