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

1 Answer
Jul 20, 2017

Answer:

Domain: #RR#

Range: #(-oo,7]#

Explanation:

The domain is the set of all possible #x#-values of that function. It is the “input” values that spew out the “output” or #y#- values of the function which make up the range. The domain of a quadratic function is usually all the real numbers (#RR#). The range will vary as in this function but we will look at that below:

Let's start by taking a look at the graph #y=x^2# which, you know, is a parabola.

The domain of #y=x^2# is #RR# or #(-oo,oo)# while the range is #[0,oo)#

graph{x^2 [-10.54, 9.46, -0.56, 9.44]}

Domain: #RR#
Range: #[0,oo)#

Now let's look at the graph of #y=-x^2#. The domain remains the same but the range is now #(-oo,0]#.

graph{-x^2 [-10.17, 9.83, -9.48, 0.52]}

Domain: #RR#
Range: #(-oo,0]#

Lastly, let's look at the graph for the function given: #y=-x^2+7# which is the function #y=x^2# reflected over the #x#-axis and shifted #7# units upward:

graph{-x^2+7 [-9.88, 10.12, -2.72, 7.28]}

Domain: #RR#
Range: #(-oo,7]#

The domain is still unchanged but the range is #(-oo,7]#