Given the graph of $ f( x)$, provide an expression for the
following functions $ h(x)$, $ g(x)$, and $ v(x)$ in terms of $ f( x)$.
{(A function $ u(x)$, say, written in terms of $ f( x)$ would be
$ u(x) = a f( {bx+c}) + d,$ where $a, b, c, $ and $d$ are constants.)}
Tags: transformations, graphing-intro, abstract-function, illustrative-example, g--a, t2, c2 This problem is good soon after students work utf03-001. They may be frustrated for a while and not know how to proceed, but I may give a hint and say, “Look at f(0) and then look at g(0). What would you have to do to f(x) in order for that to happen?” They begin visualizing how certain operations affect the original function. It’s a useful way to investigate composition because it helps them see how the “order” of operations matters.