How do you find the domain and range of #-x^2+7#?

1 Answer
Dec 29, 2017

Answer:

Domain: #x in RR#
Range: #{y|y<=7}#

Explanation:

The domain is rather simple to figure out. Since the function is defined with real numbers for all #x#, the domain will be #x in RR#.

To figure out the range of the function, we'll consider it as a parabola. The leading term is negative so it'll be concave downwards (#nn#). This means that the domain is #-oo# to whatever the vertex of the parabola is.

The vertex of the parabola #y=x^2# is at #(0,0)# and our function is that same parabola, but translated #7# units up. This means the vertex will be at #(0,7)# and this means our range is #-oo# to #7#:
#{y|y<=7}#