Cards In This Deck

• $\text{To sketch the graph of }y=f(|x|)\text{, how do you transform the graph of }y=f(x)\text{?}$
  $$\begin{gathered} \text{1. Sketch }y=f(x)\text{ for }x\ge 0\text{.} \\ \text{2. Discard the graph for }x<0\text{.} \\ \text{3. Reflect the graph for }x\ge 0\text{ in the }y\text{-axis.} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{To sketch }y=|f(x)|\text{, you discard the part of the graph where }x<0\text{ and reflect the rest.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ To sketch }y=|f(x)|\text{, you reflect the part of the graph below the x-axis (}y<0\text{) in the x-axis to make it positive.} \end{gathered}$$
• $\text{When sketching transformations, does the order matter for }y=2f(x)-1\text{?}$
  $\text{Yes. You must apply the stretch (}\times 2\text{) first, then the translation (}-1\text{).}$
• $$\begin{gathered} \text{True or False?} \\ \text{The transformation }y=f(x+a)\text{ moves the graph }a\text{ units to the right.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ It is a translation by vector } \\ \left(\begin{array}{c}\\ -a\\ \\ 0\end{array}\right) \\ \text{ (moves left if }a>0\text{).} \end{gathered}$$
• $\text{Which transformation does }y=f(ax)\text{ represent?}$
  $\text{A horizontal stretch with scale factor }\frac{1}{a}\text{.}$