Use the graph of the function f to determine the given limit.
picture below

Option: a is correct.

Limit of the function at x=2 is: 2

Step-by-step explanation:

Clearly by looking at the graph of the function we could observe that the function f(x) is defined as:

f(x)=  -x+4   when x≠4

and    8 when x=2

since we could see that the function f(x) is a line segment that passes through the point (4,0) and (0,4).

and the equation of line passing through two points (a,b) and (c,d) is given by:

Here a,b)=(4,0) and (c,d)=(0,4)

Hence,

the equation of line is:

Now the left hand limit of the function at x=2 is:

Similarly the right hand limit of the function at x=2 is:

Hence, the limit of the function at x=2 is:

2

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