How do you find domain and range for #f(x)=x^2-4x+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(x-2)# :
#" "# 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]}