Question

Which of the following functions is graphed below? Please help!!

Answer 1

The answer is choice C. 

The hole is attached to the graph for x^2+4 which means that we do NOT include this as part of the graph. The graph x^2+4 is only graphed when x < 2 is true which is what choice C says. Similarly, x+4 is only graphed when x >= 2.

Answer 2

Answer:

The correct option is C. $y=\left \{ {x^2+4, \; x$

Step-by-step explanation:

Consider the provided graph:

The graph has an open and closed dot at x = 2.

The open dot attached to the function $y=x^{2}+4$ and the closed dot attached to the function $y=x+4$.

Note, we use $\leq or \geq$ sign in order to show closed dots and < or > sign to show open dots.

By observing the graph, it is clear that the function $y=x+4$ takes all the value which are greater or equal to 2. Therefore, the function can be written as $y=x+4, x\geq 2$.

The graph of the function $y=x^{2}+4$ has an open dot at $x = 2$ which means the function can take all real values less than 2. Therefore, the function can be written as $x^2+4, x$.

Therefore, the correct option is C. $y=\left \{ {x^2+4, \; x$