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,∞).
