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

Option: A is the correct answer.

A. y= x³-3 ; x≤2

and x²+6 ; x>2

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)