Modulus of functions and reciprocal graphs Quiz

1. Solve $|3x-2|=7$.

• A. $x=3$ only
• B. $x=\frac53$ or $x=-3$
• C. $x=3$ or $x=-\frac53$
• D. $x=-3$ or $x=\frac53$

2. Solve $|x+1|>3$.

• A. $x<-4$ or $x>2$
• B. $-4<x<2$
• C. $x>2$
• D. $x<-2$ or $x>4$

3. Where does $y=\frac{1}{\mathrm{f}(x)}$ have vertical asymptotes?

• A. Where $\mathrm{f}(x)=1$
• B. Where $\mathrm{f}(x)=\infty$
• C. At the turning points of $\mathrm{f}$
• D. Where $\mathrm{f}(x)=0$

4. What is the maximum value of $y=\frac{1}{(x-2)^2+1}$?

• A. $2$
• B. $1$
• C. $\frac12$
• D. $0$

5. Solve $|x|=2x-3$.

• A. $x=1$ or $x=3$
• B. $x=1$ only
• C. $x=3$ only
• D. $x=-1$ or $x=3$