Unless specific restrictions are given, the domain of absolute value functions is usually all real numbers.
Domain:& - ∞ < x < ∞
Range
The range of absolute value functions depends on the y-coordinate of the vertex, so let's find this value first.
h(x)= |x-3|+2
In this type of functions, the vertex is the point in which the absolute value expression equals 0.
|x-3|=0 ⇔ x=3
Knowing the x-coordinate of the vertex, we are able to find its y-coordinate.
Since the y-coordinate of the vertex equals 2 and the graph opens upwards (because there is no minus sign before absolute value expression), the range of this function is all real numbers greater than or equal to 2.
Range:& y ≥ 2
Checking the Answer
To verify your answer, enter the function rule in the calculator by pushing Y= and writing the function rule in the first row. Next, by pushing GRAPH, the calculator will draw the graph of the function.
Looking at the graph, we can confirm that our solution is correct.
