Transformations/ Images — Quiz 5

Questions in this quiz (6)

1. Question 1

   • -2
   • 0
   • 1
   • 2

2. Which of these is $$y=e^{x-2}+5$$ reflected about the $$y$$-axis?

   • $$y=e^{-x-2}+5$$
   • $$y=e^{-x+2}+5$$
   • $$y=-e^{x-2}+5$$
   • $$y=e^{2-x}+5$$

3. In the standard $$(x,y)$$ coordinate plane, the endpoints of $$\overline{CD}$$ are $$(-p,q)$$ and $$(r,-s)$$, where $$p,q,r,$$ and $$s$$ are distinct positive real numbers. Line segment $$\overline{C'D'}$$ is the image of $$\overline{CD}$$ after a reflection across the $$y$$-axis. What are the coordinates of the endpoints of $$\overline{C'D'}$$?

   • $$(-p,q)$$ and $$(-r,s)$$
   • $$(p,q)$$ and $$(r,-s)$$
   • $$(p,q)$$ and $$(-r,-s)$$
   • $$(p,-q)$$ and $$(-r,s)$$

4. The functions $$f(x)=\cos x$$ and $$g(x)=\cos(x-\frac{\pi}{3})+1$$ are graphed in the standard $$(x,y)$$ coordinate plane. Which of the following sequences of transformations could be applied to $$f(x)$$ such that the image of the graph of $$f(x)$$ is the graph of $$g(x)$$?

   • Shift right by 1, then shift down by $$\frac{\pi}{3}$$
   • Shift left by 1, then shift down by $$\frac{\pi}{3}$$
   • Shift right by $$\frac{\pi}{3}$$, then shift up by 1
   • Shift left by $$\frac{\pi}{3}$$, then shift up by 1

5. A circular park is represented by the equation: $$x^2+y^2-8x+6y+9=0$$. The park's location is being adjusted by moving it 3 units to the left and 4 units up. What is the equation of the new park boundary after this transformation?

   • $$(x-1)^2+(y+1)^2=16$$
   • $$(x-1)^2+(y-1)^2=16$$
   • $$(x+1)^2+(y-1)^2=4$$
   • $$(x-1)^2+(y-1)^2=4$$

6. Given an arbitrary equation $$f(x, y) = 0$$ find another equation that is symmetric to it with respect to the line$$x - y + 4 = 0$$

   • $$f(4 - y,\ x - 4)= 0$$
   • $$f(4 + y,\ x - 4)= 0$$
   • $$f(4 + y,\ x + 4) = 0$$
   • $$f(-4 + y,\ x + 4) = 0$$