Transformations of graphs Quiz

1. The graph of $y=f(x)$ is transformed to $y=f(x-4)$. What is the transformation?

• A. translation $4$ units to the left
• B. translation $4$ units up
• C. translation $4$ units to the right
• D. stretch with scale factor $4$

2. Which transformation maps $y=f(x)$ onto $y=f(3x)$?

• A. stretch parallel to the $x$-axis, scale factor $\frac13$
• B. stretch parallel to the $x$-axis, scale factor $3$
• C. stretch parallel to the $y$-axis, scale factor $3$
• D. translation $3$ units to the left

3. The point $(4,6)$ lies on $y=f(x)$. Which point lies on $y=f(2x)$?

• A. $(8,6)$
• B. $(4,12)$
• C. $(4,3)$
• D. $(2,6)$

4. What is the maximum value of $y=\cos x+2$?

• A. $2$
• B. $3$
• C. $1$
• D. $4$

5. What is the smallest positive $x$ at which $y=\tan2x$ has an asymptote?

• A. $180^\circ$
• B. $90^\circ$
• C. $45^\circ$
• D. $22.5^\circ$