Graph of a piecewised function is f(x)=1, x>0 and f(x)=-1, x<0
What is the lim f(x)=? x-->-3
I did the following:
My f(x)=1, x>0 graph started from the point (0,1) and extended right infinitely. My (x)=-1, x<0 graph extended from the point (0,-1)infinitely toward the left in a straight line. {{{is this wrong so far???}}}
Then I reasoned that since the lines are not coming near each other at all around x-->-3 the limit is undefined.
I know the correct answer is lim f(x)=-1 as x-->-3 but how do I get that???
To find the limit of a function as x approaches a specific value, we need to consider the behavior of the function as x gets closer and closer to that value.
In the case of the given piecewise function f(x)=1, x>0 and f(x)=-1, x<0, we can approach the limit as x->-3 by looking at the behavior of the function on both sides of -3.
On the left side of -3, the function is defined as f(x)=-1 for x<0. Since x is approaching -3 from the left side, which is less than 0, the function value is -1 for all values close to -3 from the left side.
On the right side of -3, the function is defined as f(x)=1 for x>0. However, since we are approaching -3 from the left side, the right-side part of the function is not relevant to determining the limit.
Therefore, as x approaches -3, the function approaches -1. Hence, the limit of f(x) as x approaches -3 is equal to -1.
In summary, to find the limit, consider the behavior of the function on both sides of the given value. In this case, by recognizing the piecewise definition of the function and evaluating the function from the left side as x approaches -3, we find that the limit is -1.