| utf03-001 The graph of $ f( x)$ is given below. Use it to graph the following. \begin{alignat*}{4} &a) f( {3x}) & &b) f( {-x}) & &c) f( {-2x}) & &d) f( {x-1})\\ &e) f( {x}) + 1 & &f) 5 f( {x}) & &g) f( {x+2}) & &h) 5 f( {3x+2}) + 1 \end{alignat*} i) In your own words, describe the manner in which the graph of $ f( x)$ changes when we: multiply $ f( x)$ by a constant; add a constant to $ f( x)$; multiply $x$ by a constant; add a constant to $x$. j) Describe the process of drawing $ u(x) = a f( {bx+c}) + d,$ where $a, b, c, $ and $d$ are constants when given only the graph of $ f( x)$. |
| utf03-004 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.)} |