Answer:
Step-by-step explanation:
We have a piesewise function composed of three pieces. two line segments and one point.
The first line cuts at point (0,0) and ends at point (3, -1)
If we use these two points we can find the equation of the line.
The slope m is:
So the equation is:
As the line cuts in (0,0) then and the equation is:
The equation of the second line is:
Now we can find f(x) (although it is not necessary to find the equation of f(x) because we have its graph)
if
;
if
;
if
.
The limit of f(x) when x tends to 3 from the left is the limit of the function when x approaches 3 from the left. If x approaches 3 from the left then
. If
then f(x) is given by the line
. Then the limit is -1 as seen in the graph
