Explain in your own words what:
lim f(x) = 5
The Attempt at a Solution
"As x approaches 2, the limit of the function f(x) is 5 (in other words, f(x) approaches 5). The value of the function that is limited can be different than the limit of the function itself."
But I do not know if there can be a function value but with an undefined limit. I also want to say above that a function value may or may not be the same as the limit, and that either value may be undefined. But I don't know for sure if that is true.
For example, what is:
lim f(x) if f(x) = x (in other words, if y = x)
Above we have a straight line graph with a slope of 1, and a y-intercept of 0.
But is the limit really 1? Even though the graph goes right through f(x) = 1?