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Functions and Relations Questions - All Grades

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Grade 9 Functions and Relations
Given f(x)=x + 1, find f(2r).
  1. 3r
  2. 3rx + 1
  3. 2rx
  4. 2r + 1
Grade 11 Functions and Relations
If y = f(x) is transformed to y = f(x) - 2, the function                     .
  1. shifts right 2 units
  2. shifts down 2 units
  3. shifts left 2 units
  4. shifts up 2 units
Grade 9 Functions and Relations
When y is written as f(x).
  1. Function Rule
  2. Function Notation
  3. Function Variable
Grade 11 Functions and Relations
Find the domain of the composite function [math](f@g)(x) if f(x)=x^2 and g(x)=sqrt(x+2)[/math].
  1. [math](-oo,oo)[/math]
  2. [math](-2,oo)[/math]
  3. [math][-2,oo)[/math]
  4. [math](-oo,-2)[/math]
Grade 10 Functions and Relations
Grade 11 Functions and Relations
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]
Grade 11 Functions and Relations
Which function matches the following description?
An absolute value function that has been reflected about the x-axis, and then shifted up 5 units.
  1. [math]f(x)=|x|+5[/math]
  2. [math]f(x)=-|x| +5[/math]
  3. [math]f(x)=-|x+5|[/math]
  4. [math]f(x)=-|x-5|[/math]
Grade 11 Functions and Relations
Grade 11 Functions and Relations
Describe the symmetry of the function. Justify algebraically.
[math]f(x)=1/x^2+3[/math]
  1. Symmetric about the x-axis
  2. Symmetric about the y-axis
  3. Symmetric about the origin
  4. No symmetry
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Let [math]f(x) = 3x^2-5x and g(x)=sqrt(x+2)[/math]. Find [math](g@f)(x)[/math].
  1. [math]3(x+2) - 5sqrt(x+2)[/math]
  2. [math]sqrt(3x^2-5x+2[/math]
  3. [math]-2x + 6[/math]
  4. [math]sqrt(3)x - (sqrt(5) -1) sqrt(x)[/math]
Grade 10 Functions and Relations
Grade 11 Functions and Relations
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
Grade 11 Functions and Relations
Find the inverse for the following function:
[math]f(x)=-3/4x+5[/math]
  1. [math]f^-1(x)=(3x-5)/4[/math]
  2. [math]f^-1(x)=3/4(x-5)[/math]
  3. [math]f^-1(x)=(-4x-5)/3[/math]
  4. [math]f^-1(x)=(-4x+20)/3[/math]
Grade 11 Functions and Relations
Determine whether the function shown has an inverse that is a function.
Graph - Quadratic Function y=2x^2
  1. Yes, the inverse is a function.
  2. No, the inverse is not a function.
Grade 11 Functions and Relations
What is the range of the function {(5,1)(6,2)(7,3)} ?
  1. {1,2,3}
  2. {5,6,7}
  3. {1,2,3,5,6,7}
  4. {1,7}
Grade 11 Functions and Relations
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
Grade 11 Functions and Relations
If y = f(x) is transformed to y = f(0.5x), the function                       .
  1. shifts left 0.5 units
  2. shifts right 0.5 units
  3. becomes "skinnier"
  4. becomes "fatter"
Grade 11 Functions and Relations
If y = f(x) is transformed to y = 0.5f(x), the function                      .
  1. becomes "skinnier"
  2. becomes "fatter"
  3. shifts up 0.5 units
  4. shifts down 0.5 units
Grade 10 Functions and Relations
What is the name of this parent function?
Graph - Absolute Function y=|x|
  1. linear
  2. square root
  3. quadratic
  4. absolute value
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