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This printable supports Common Core Mathematics Standard HSF-BF.B.4, HSF-BF.B.4d

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Inverse Functions and Domain Restrictions (Grade 10)

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Inverse Functions and Domain Restrictions

1. 
For the function [math]f(x) = 3(x-2)^2[/math], which of the following domain restrictions would cause [math]f(x)[/math] to be invertible? There may be more than one correct answer.
  1. [math]x > 2[/math]
  2. [math]x>= 2[/math]
  3. [math]x > -2[/math]
  4. [math]x < 0[/math]
2. 
Let [math]f(x)[/math] be the quadratic function in the graph below. Assume that the horizontal axis represents [math]x[/math] values and the vertical axis [math]y[/math] values. Which of the following domain restrictions on [math]f(x)[/math] would make it invertible? There may be more than one correct answer.
Graph - Quadratic Function y=1/2x^2
  1. [math]x>2[/math]
  2. [math]x<2[/math]
  3. [math]x > -4[/math]
  4. [math]x<=0[/math]
3. 
For the function [math]f(x) = x^2 - 9[/math], which of the following domain restrictions would make it invertible? There may be more than one correct answer.
  1. [math]x<=0[/math]
  2. [math]x<3[/math]
  3. [math]x>=3[/math]
  4. [math]x > -3[/math]
4. 
For the quadratic function in the graph below, which of the following domain restrictions would make it invertible? There may be more than one correct answer. Assume that the horizontal axis represents [math]x[/math] values and the vertical axis [math]y[/math] values.
Graph - Quadratic Function y=-2x^2
  1. [math]x<1[/math]
  2. [math]x < -4[/math]
  3. [math]x>=5[/math]
  4. [math]x<0[/math]
5. 
If [math]f(x) = 6(x-4)^2+8[/math], which of the following domain restrictions would make it invertible? There may be more than one correct answer.
  1. [math]x<= 8[/math]
  2. [math]x>0[/math]
  3. [math]x>= -4[/math]
  4. [math]x>4[/math]
6. 
For the absolute value function [math]f(x)[/math] pictured in the graph, which of the following domain restrictions would make it invertible? There may be more than one correct answer. Assume that the x- and y-axes have a scale of one unit.
Graph - Absolute Function y=|1/2x|
  1. [math]x>=1[/math]
  2. [math]x<=0[/math]
  3. [math]x<0[/math]
  4. [math]x<-3[/math]
7. 
For the function [math]f(x) = x^2 + 4x +5[/math], which of the following domain restrictions would make it invertible?
  1. [math]x < -1[/math]
  2. [math]x<= -2[/math]
  3. [math]x < 2[/math]
  4. [math]x>=0[/math]
8. 
Given the function [math]f(x) = 2x^2 + 28x + 90[/math], which of the following restrictions on the domain of [math]f(x)[/math] would make it invertible? There may be more than one correct answer.
  1. [math]x < 90[/math]
  2. [math]x >= -8[/math]
  3. [math]x < -7[/math]
  4. [math]x < 0[/math]
9. 
Let [math]f(x)[/math] be the function pictured in the graph below. Assume that the domain of the function is [math]x in [0,10][/math]. Also, assume that the scale of the x- and y-axes is one unit. Which of the intervals specified below which would make [math]f(x)[/math] invertible? There may be more than one correct answer.
Graph - Piecewise Random 1
  1. [math](0,6)[/math]
  2. [math][2,6] uu (9,10)[/math]
  3. [math](6,8)[/math]
  4. [math](0,2) uu (6,8)[/math]
10. 
Let [math]f(x) = 3(x-5)^2[/math]. Which of the following domain restrictions makes [math]f(x)[/math] invertible and ensures that [math]f^{-1}(x)[/math] has no maximum value?
  1. [math]x>0[/math]
  2. [math]x>5[/math]
  3. [math]x<5[/math]
  4. [math]x<-5[/math]

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