Question

Determine where the function f(x) = 3x - 2 is continuous. The function is continuous on (Simplify your answer. Type your answer in interval notation.)

Answer 1

Answer:

f(x) is continuous over the R, which is (-∞,∞)

Step-by-step explanation:

According to the definition of continuity, a function f(x) is continuous over the interval [a,b] if f(c), c ∈ [a,b], exists.

There is no constraint or restriction in the domain of the function, that is, every number may be plugged in and get a result.

However, there is another condition to be satisfied in order to tell if the f(x) is continuous:

$\lim_{x \to c} f(x) =f(c)$

That implies that the limit has to exist and has to be equal to f(c).

As we can see in the picture the function does not have any break over the shown region.

So we can take a number c, and plug it into f(x) and we get:

$f(x) = 3x - 2\\f(c) = 3c - 2$

Then we calculate the limit

$\lim_{x \to c} f(x) = \lim_{x \to c} 3x-2 =3c-2$

Because the limit exists and equals to f(c) we can say the function is continuous over R that is (-∞,∞).