Graph the function. State the domain and range and describe how to graph is related to the graph of g(x)= |x|

Question

This is the equation f(x) = -4|x-2|+3

Answer 1

It is first essential to understand what g(x) looks like. This is the absolute value graph which appears as a "V" with the bottom of the "V" at (0,0). The graph has a slope of 1, and a range (y-values) of [0,infinity), and a domain of (-infinity, infinity).

When we manipulate this graph, we can change the way it appears. In f(x) the slope of the graph is negative, so the "V" appears upside down. f(x) has a slope of 4, which means that the slope of the lines are steeper than in g(x) and the "V" is narrower. f(x) is also translated. The -2 which appears within the absolute value lines indicates that the graph is shifted to the right by 2, and the +3 outside of the absolute value lines indicates the graph has been shifted up by 3.