The range of the function is all possible values of y.

Since f(x) = 3x + 4 is a linear function, the range would be all real numbers.

All Real Numbers, or ` (-oo,+oo) `

You should evaluate the limits of the function to `+-oo` , such that:

`lim_(x->-oo)(3x + 4) = 3*lim_(x->-oo)(x) + 4 = 3*(-oo) + 4 = -oo`

`lim_(x->oo)(3x + 4) = 3*lim_(x->oo)(x) + 4 = 3*(oo) + 4 = oo`

Since the function is continuous, hence, the range of the function is `(-oo,+oo).`

You also may notice that the graph of the function `f(x) = 3x + 4` , that is the line, is continuous and it goes up at x increases from `-oo ` to `+oo.`

Hence, evaluating the range of the function yields `f(x) = y in (-oo,+oo).`