Question

Prove that the function f(x) = 5x - 3 is continuous at x = 0, at x = -3 and x = 5

Answer 1

plug in each of those values for x to come up with your y value. When x is 0, y = -3, when x = -3, y= -18, when x = 5, y = 22

Answer 2

Thank you for responding and my apologies for the late response.

I understand but how does that prove that the function is continuous?

Answer 3

*my 2 cents*

1) Theoretically, we prove that a function ( let's call it f(x) ) is continuous in a point/value (let's call this point "p") by proving that :

lim of f(x) as x -> p from (-infinity) = lim of f(x) as x -> p from (infinity) = f(p).

Or easier : lim of f(x) as x-> p = f(p).

Which reduces this particular problem to : lim of 5x-3 as x -> p = 5p - 3 = f(p) (obviously) and that's it.

2) However, you can also write that linear functions are continuous by definition unless there are special restrictions in the domain or range. If the actual domain and range of any real function ( f(x) = ax + b ) is R, then it is and forever will be continuous (it would be too generous to include the discussion @ 1) but it's basically a known thing like 2+2=4)