**Domain:**

#x^2+4x-21# is a polynomial. I don't need to worry about dividing by zero or taking even roots or negative numbers or other weirdness. The domain is all real numbers. (The interval #(-oo, oo)#

**Range**

This may depend on ow much you know. I would graph (or at least think about the graph) of the parabola whose equation id #y=x^2+4x-21#

For #y=ax^2+bx+c#,

The vertex is at #x=(-b)/(2a)# In this case the vertex is at #x=-4/(2(1))=-2#

For this value of #x=-2#, we have #y=(-2)^2+4(-2)-21=4-8-21=-25#

#a>0# tells me that the parabola opens upward, so the #y# values (the range) are all values greater than or equal to -25. The range is #[-25, oo)#

Here's the graph (you may need to zoom in to see some points. (Use your mouse wheel)

graph{x^2+4x-21 [-75.07, 73, -58.35, 15.8]} :