Let f (a function)

Question

Let f be a function such that . Which statement best interprets this limit?

The function f has a value of –5 when x is 5.

The function f has a value approaching –5 as x approaches 5.

The function f has a value approaching –5 as x approaches –5.

The function f has a value approaching –5 as x approaches 5 from the left.

Answer 1

The "x → 5^- " means that when you pick values of x closer and closer to 5 FROM THE LEFT (hence the negative symbol), the function values get closer and closer to -5

Example, If you pick x = 4, perhaps the function value is -4.5. If you pick x = 4.9, perhaps the function value -is -4.95. If you pick x = 4.99, perhaps the function value is -4.995, etc. You are not allowed to pick x = 5.01 because that value of x is past 5, You can pick values like 4.999999 though.