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,∞).

i would be happy to . most people on would also love to i'm sure. if you just want someone who has done algebra before and want a little more personal relationship than just begging strangers for , i can certainly be of service. i do have college myself so i might not be 24/7.

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.