Cards In This Deck

• $\text{How do you find the asymptotes of a transformed reciprocal graph like }y=\frac{1}{x-2}+1\text{?}$
  $\text{Shift the vertical asymptote to where denominator is zero (}x=2\text{) and horizontal asymptote to the vertical shift (}y=1\text{).}$
• $\text{What transformation does }y=f(ax)\text{ represent?}$
  $\text{Horizontal stretch by scale factor }\frac{1}{a}\text{.}$
• $$\begin{gathered} \text{True or False?} \\ \text{The transformation }y=-f(x)\text{ reflects the graph in the y-axis.} \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: It reflects in the x-axis.} \end{gathered}$$
• $\text{What transformation does }y=af(x)\text{ represent?}$
  $\text{Vertical stretch by scale factor }a\text{.}$
• $$\begin{gathered} \text{True or False?} \\ \text{To stretch }y=x^2+1\text{ horizontally by scale factor 2, you write }y=2(x^2+1)\text{.} \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: }y=(\frac{1}{2}x{)}^2+1 \end{gathered}$$
• $\text{When sketching }y=2\cos x\text{, which feature of the graph changes?}$
  $\text{The amplitude (vertical stretch).}$
• $\text{When sketching }y=f(x)+a\text{, how does the graph move?}$
  $\text{Translate vertically by vector }\left(\begin{array}{c}0\\ a\end{array}\right)\text{ (up by }a\text{).}$
• $\text{When sketching }y=f(x+a)\text{, how does the graph move?}$
  $\text{Translate horizontally by vector }\left(\begin{array}{c}-a\\ 0\end{array}\right)\text{ (left by }a\text{).}$
• $\text{What is the first step to sketch }y=\sin (x+30^{\circ })\text{?}$
  $\text{Start with the standard }y=\sin x\text{ graph and translate it.}$