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

1 Answer
Jan 14, 2018

Answer:

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

Explanation:

Finding the Domain
The domain is where the function is defined in terms of real numbers. This function is always defined, so the domain is all real numbers, #RR#.

Finding the Range
The range is the possible values that the function takes on. If we consider the function as a parabola, we can see that it will be concave downwards (#nn#) because of the negative leading coefficient

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