Sketching graphs of functions Quiz

1. Which describes the graph of $y=\frac{5}{x^2}$?

• A. first and third quadrants
• B. above the $x$-axis, in the first and second quadrants
• C. second and fourth quadrants
• D. below the $x$-axis

2. For $0^\circ\le x\le360^\circ$, where are the asymptotes of $y=\tan x$?

• A. $0^\circ$ and $180^\circ$
• B. $45^\circ$ and $225^\circ$
• C. $180^\circ$ and $360^\circ$
• D. $90^\circ$ and $270^\circ$

3. How does the curve $y=(x+1)(x-2)^2$ behave on the $x$-axis?

• A. crosses at $x=-1$ and touches at $x=2$
• B. touches at $x=-1$ and crosses at $x=2$
• C. crosses at both
• D. touches at both

4. How many solutions does $\sin x=0.5$ have for $0^\circ\le x\le360^\circ$?

• A. $3$
• B. $4$
• C. $2$
• D. $1$

5. How many real solutions does $x^3=\frac1{x^2}$ have?

• A. $0$
• B. $1$
• C. $2$
• D. $5$