What are the differences between the two functions? What are the possible x- and y-values?
Graph:
Description: The graph of v is a horizontal translation 5 units right of the graph of f. Domain: All real numbers. Range: y≥0
Practice makes perfect
To graph v(x), let's take a closer look at its equation.
v(x)=|x-5|
The given equation is a transformation of the parent function f(x)=|x|.
We can see that 5 is subtracted from the x-value. Therefore, the graph of v(x) is a horizontal translation 5 units right of the graph of f(x).
To find the domain and range of an absolute value function, we need to consider the location of the vertex. Because this type of function always has the same basic V-shape, the y-value of the vertex is the minimum or maximum of the range. The minimum of the given function is 0 and then it will continue increasing indefinitely.
Range: y≥ 0
The domain of an absolute value function is usually be all real numbers, unless specific restrictions have been imposed upon the function.
Domain: all real numbers
