How do you find domain and range for #f(x)=x^24x+7 #?
1 Answer
Domain:
Range:
Explanation:
Given:
Unless a function is limited, the domain is all reals.
Quadratic functions which are graphs of parabolas have a maximum or minimum, the vertex. This vertex determines the range values.
If the equation is in the from
vertex:
Range:
Graph of
graph{x^2  4x + 7 [5, 5, 2, 10]}
Here are some examples of functions that are limited in domain and range:

Contains a square root:
#sqrt(x2)# :
#" "# Domain:#x >= 2; " Range: " y >= 0#
graph{sqrt(x  2) [2, 5, 2, 5]} 
Rational functions:
#x/(x+4):" "# contain asymptotes
#" "# Domain:#x != 4; " Range: " y != 1#
graph{x/(x+4) [15, 5, 10, 10]} 
Exponential functions:
#2^x# :
#" Domain: all reals; Range: " y>0#
graph{2^x [5, 10, 10, 30]}