Question

Which of the following functions is graphed below

Answer 1

A!
the easiest way would be to just look at the inequality parts.
the equation that is on the left has a filled in circle at 2, so it must be
$\leqslant 2$
and the equation on the right has an open circle so it must be just
$> 2$

Answer 2

Answer:

Option: A is the correct answer.

A.        y=    x³-3  ;  x≤2

         and   x²+6  ; x>2

Step-by-step explanation:

By looking at the graph we observe that the cubic function is defined in the interval (∞,2]

Since, there is a closed circle at x=2 in the graph of the cubic function.

Also, the function f(x) is defined for x≤2 by:

f(x)=  x³-3

at x=2 we have:

f(2)=2³-3

i.e.

f(2)=8-3

i.e.

f(2)=5

i.e. there is a closed circle at (2,5)

Also, for x>2 the graph is defined of a quadratic function.

and the function is given by:

f(x)=x²+6

Also, at x=2

we have:

f(2)=2²+6

i.e.

f(2)=10

This means that there is a open circle at (2,10)