Transformations of Functions — Advanced Math

Questions in this quiz (7)

1. If $$f(x)=x^2$$ which function represents the graph of $$f(x)$$ shifted up $$3$$ units?

   • $$y=x^2+3$$
   • $$y=x^2-3$$
   • $$y=(x+3)^2$$
   • $$y=(x-3)^2$$

2. The graph of $$y=(x+4)^2$$ is obtained by shifting the graph of $$y=x^2$$:

   • 4 units right
   • 4 units left
   • 2 units right
   • 2 units left

3. If $$f(x)=x^3$$, what is the equation of the graph reflected over the $$x$$-axis?

   • $$y=f(x)$$
   • $$y=-f(x)$$
   • $$y=f(-x)$$
   • $$y=-2f(-x)$$

4. The reflection of $$y=f(x)=e^x$$ over the $$y$$-axis is:

   • $$y=e^x$$
   • $$y=-e^x$$
   • $$y=e^{-x}$$
   • $$y=-e^{-x}$$

5. If $$f(x)=x^2$$ which equation represents a horizontal compression by a factor of $$\frac{1}{2}$$?

   • $$y=f(2x)$$
   • $$y=f(\frac{x}{2})$$
   • $$y=2f(x)$$
   • $$y=\frac{1}{2}f(x)$$

6. A graph of $$y=f(x)$$ passes through $$(2,5)$$. If the new function is $$g(x)=f(x)+4$$, what point lies on $$g(x)$$?

   • $$(2,1)$$
   • $$(2,4)$$
   • $$(2,5)$$
   • $$(2,9)$$

7. The temperature in °F is modeled by $$T(t)=60+10\sin(t)$$ where $$t$$ is time in hours. What transformation changes the average temperature from 60°F to 70°F?

   • Add 10
   • Subtract 10
   • Replace $$t$$ with $$t+10$$
   • Multiply by 10