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Function Transformations II (Grades 11-12)

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Function Transformations II

1. 
Which of the following is not a parent function?
  1. [math]f(x)=x^2[/math]
  2. [math]f(x)=|x|+1[/math]
  3. [math]f(x)=x[/math]
  4. [math]f(x)=x^6[/math]
2. 
What best describes the transformation from [math] f(x) = x^2 [/math] to [math]f(x)=-(x^2)[/math]?
  1. Reflect about the x axis
  2. Reflect about the y axis
  3. Stays the same
  4. Moves down 1
3. 
For the function [math]f(x)=1/3x^3[/math], choose the best description of the transformation that has been applied to the parent function.
  1. Vertical compression
  2. Vertical stretch
  3. Horizontal compression
  4. Horizontal stretch
4. 
Which of the following describes a quadratic function that has been shifted to the left 4 units?
  1. [math]f(x)=x^2 +4[/math]
  2. [math]f(x)=x^2-4[/math]
  3. [math]f(x)=(x-4)^2[/math]
  4. [math]f(x)=(x+4)^2[/math]
5. 
The function [math]f(x)=|x+2| -3[/math] translates the graph of the absolute value parent function                 2 units and                 3 units.
  1. up, down
  2. left, right
  3. up, right
  4. left, down
6. 
How is the graph of [math]g(x)=|x-3| +1[/math] related to the parent function [math]f(x)= |x| ?[/math]
  1. Moves right 3, moves down 1
  2. Moves right 3, moves up 1
  3. Moves left 3, moves down 1
  4. Moves left 3, moves up 1
7. 
How is the graph of [math]g(x)=|x+4| -2[/math] related to the parent function [math]f(x)=|x| ?[/math]
  1. Moves right 4, moves down 2
  2. Moves right 4, moves up 2
  3. Moves left 4, moves down 2
  4. Moves left 4, moves up 2
8. 
Which most accurately describes how you would transform this function?
[math]f(x)=(x+3)^2-4[/math]
  1. Move the quadratic parent function left 3 then down 4
  2. Move the quadratic parent function left 4 then down 3
  3. Move the quadratic parent function right 3 then down 4
  4. Move the quadratic parent function right 4 then down 3
9. 
In the function [math]f(x)=|x-h|+k[/math], what values of h and k ensure that the vertex of the graph of the function appears in the 3rd quadrant?
  1. [math]h>0, k>0[/math]
  2. [math]h>0, k<0[/math]
  3. [math]h<0, k>0[/math]
  4. [math]h<0, k<0[/math]
10. 
Which of the following could identify the transformation of a parabola with a vertex of (-4,-6) to a parabola with a vertex of (1,-6)?
  1. [math]f(x)+5[/math]
  2. [math]5f(x)[/math]
  3. [math]f(x+5)[/math]
  4. [math]f(x-5)[/math]
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