Use the definition of continuity to determine whether f is continuous at a = 5.

Question

f(x) = 8x + 1

Is f continuous at 5?

Answer 1

Hi,

f(x) = 8x + 1

First , this is a linear function and you can answer, " all linear functions are continuous so this function at a= 5 is continuous."

But if you want to show any function is continuous you need to do 3 steps,

step 1, you show exist f(a) ========> f(5) = 8*5 +1 = 41

step 2, you need to find, limit of function when x approaches to a ( given number) ==> lim f(x) = 8(5) +1 =41

step 3, you need to show step1 and step2 are equal ====> in this case you see f(5) = 8*5 +1 = 41=lim f(x)

so this function is continuous

if for any reason one of 3 steps is not true it means that function is not continuous.

I hope it is useful,

Minoo