- Identify where the graph \(f(x)=\dfrac{\abs{x}}{x}\) is not continuous. (1 mark)
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- Sketch the graph of \(f(x)\). (2 marks)
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Show Answers Only
a. \(\text {Denominator} \neq 0\)
\(f(x)\ \text{is not continuous when} \ \ x=0\)
b. \(\text{If} \ \ x>0 \ \Rightarrow \ f(x)=\dfrac{x}{x}=1\)
\(\text{If} \ \ x<0 \ \Rightarrow \ f(x)=-\dfrac{x}{x}=-1\)
Show Worked Solution
a. \(\text {Denominator} \neq 0\)
\(f(x)\ \text{is not continuous when} \ \ x=0\)
b. \(\text{If} \ \ x>0 \ \Rightarrow \ f(x)=\dfrac{x}{x}=1\)
\(\text{If} \ \ x<0 \ \Rightarrow \ f(x)=-\dfrac{x}{x}=-1\)