| 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)$. |
| utf03-003 Let $S$ be the relation $ \{ (x,y) | (x^2-4)y= x^2 + 2x \}$.
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| utf03-005 Given that $ f( x)$ is a function that has x-intercepts at $x=0, x=2, $ and $x=-2$; y-intercept $(0,0)$; horizontal asymptote $y=-1$; and vertical asymptotes at $x=3$ and $x=-3$.
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| utf03-006 Which of the graphs below could correspond to the following functions? {Match them.} \begin{alignat*}{4} &a) \text{odd power function}\hphantom{\text{log x}} & &b) \text{ even power function} & &c) \text{a quadratic}\\ &d) \log x & &e) \text{a 4th degree polynomial} & &f) b^x \\ &g) \sin x & &h) (\frac{1}{ 2})^x & &i) \text{absolute value} \end{alignat*} |
| utf19-002 For each, sketch a graph with the given properties. |