The graph of f(x) is obtained by reflecting the graph of g(x)=3|x| over the x-axis.Which equation describes f(x)?A) f(x)=3|x|B) f(x)= -3|x|C) f(x)= |x+3|D) f(x)= - |x+3)

Accepted Solution

Answer:Choice B), [tex]f(x) = -3|x|[/tex].Step-by-step explanation:Each point on the graph of [tex]g(x)[/tex] can be represented as [tex](x, g(x))[/tex].When the graph of [tex]g(x)[/tex] is reflected over the x-axis, each point on the graph is also reflected over the x-axis. The x-coordinate of each point will not change but the sign in front of the y-coordinate will flip. For example, [tex]1[/tex] (same as [tex]+1[/tex]) will become [tex]-1[/tex], and vice versa. In general, [tex](x, g(x))[/tex] will become [tex](x, -g(x))[/tex].On the other hand, points on the graph of [tex]f(x)[/tex] can be represented as [tex](x, f(x))[/tex]. [tex]f(x)[/tex] is the reflection of [tex]g(x)[/tex], so [tex](x, -g(x))[/tex] and [tex](x, f(x))[/tex] shall be equivalent. In other words, [tex]f(x) = -g(x) = - 3|x|[/tex].