If possible, find all values of a such that there are no x-intercepts for f (x) = 3|x + 4| +

a. (enter your answer using interval notation. If an answer does not exist, enter dne.)

We are given function f (x) = 3|x + 4| + a.

And it is said that a should be all those values such that there are no x-intercepts for given function f (x).

We know, the standard absolute function f (x) = a|x-h| have an x-intercept at (h, 0).

But if we write fuction in form f (x) = a|x-h|+k, the value of k represents k units up or down of the x-axis.

We could also say, if we have value k other than 0, it will never touch (or cut) the x-axis.

With respect to the given function the k is take by a variable.

So, the value of a can't be 0.

Therefore, we can write interval notation for a values as

(-∞,0) ∪ (0,∞).