Cards In This Deck

• $\text{When solving }|f(x)|=n\text{ where }n\text{ is a constant, what condition must }n\text{ satisfy for solutions to exist?}$
  $n\ge 0$
• $$\begin{gathered} \text{True or False?} \\ \text{The solution to the inequality }|x|>a\text{ (where }a>0\text{) is }x>a\text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ The solution is }x>a\text{ OR }x<-a\text{.} \end{gathered}$$
• $\text{Definition of the modulus function }|x|$
  $$\begin{gathered} |x|=x\text{ if }x\ge 0 \\ |x|=-x\text{ if }x<0 \end{gathered}$$
• $\text{First step to solve an equation involving a modulus function, e.g., }|2x-1|=x+5\text{?}$
  $\text{Sketch the graphs of }y=|2x-1|\text{ and }y=x+5\text{ to see how many intersection points exist.}$
• $\text{To sketch the graph of }y=f(|x|)\text{, how do you transform the graph of }y=f(x)\text{?}$
  $$\begin{gathered} \text{1. Sketch }y=f(x)\text{ for }x\ge 0\text{.} \\ \text{2. Discard the graph for }x<0\text{.} \\ \text{3. Reflect the graph for }x\ge 0\text{ in the }y\text{-axis.} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{To sketch }y=|f(x)|\text{, you discard the part of the graph where }x<0\text{ and reflect the rest.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ To sketch }y=|f(x)|\text{, you reflect the part of the graph below the x-axis (}y<0\text{) in the x-axis to make it positive.} \end{gathered}$$