What is range of f(x)=-1/4 |x-3|+5

Question

what is the rang of f(x)=-1/4|x-3|+5

Answer 1

This function is the transformation of f(x) = | x |.

 

The vertex of this given function is (3, 5).  So you have an upside down V-shape graph with vertex of (3,5).

 

Since the range is the set of defined y values on the graph, the range is in the interval (-∞,5).