Question

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

Answer 1

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,∞).