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

Question

Abigail Allen · Accepted Answer

Domain: #RR#

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

Eva Adamson · Answer

undefined To find the domain and range of the function -x^2 + 7:

Domain: All real numbers (-∞, +∞)
Range: All real numbers from -∞ to 7, inclusive. (−∞, 7]