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Functions and Relations Questions - All Grades

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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
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(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 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
Let [math]f(x) = 5x-1 and g(x) = 3x^2 + 2x - 1[/math]. Find [math](g@f)(x)[/math].
  1. [math]75x^2 - 20x[/math]
  2. [math]15x^2+10x-6[/math]
  3. [math]75x^2-28x+2[/math]
  4. [math]25x-3[/math]
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 11 Functions and Relations
Let [math]f(x) = 5x-2 and g(x)= (3x)/ (2+x) [/math]. Find [math](g@f)(x)[/math].
  1. [math](15x)/(x+2) - 2[/math]
  2. [math](15x)/(2+5x)[/math]
  3. [math] (3x(5x-2))/(x+2)[/math]
  4. [math](15x-6)/(5x)[/math]
Grade 11 Functions and Relations
If [math] g(x) = 4/(2-x) and (g@f)(x) = -2/x^2[/math], find [math]f(x)[/math].
  1. [math](2x^2)/(x^2+1)[/math]
  2. [math](x-2)/x^2[/math]
  3. [math]2x^2 + 2[/math]
  4. [math]-1/(2(x^2 - 2))[/math]
Grade 11 Functions and Relations
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 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
Does the function shown here have an inverse that is also a function?
Graph - Exponent Function y=2^x
  1. Yes, the inverse is a function.
  2. No, the inverse is not a function.
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
Identify the one-to-one function:
  1. [math]{(-1,4), (2,7), (-1,9), (5,0)}[/math]
  2. [math]{(-1,4), (3,-6), (-5,6), (1,4)}[/math]
  3. [math]{(3,-4), (-5,9), (2,7), (-1,8)}[/math]
  4. [math]{(-6,5), (2,3), (-3,3), (1,0)}[/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
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
Grade 11 Functions and Relations
If y = f(x) is transformed to y = f(x + 2), the function                     .
  1. shifts up 2 units
  2. shifts down 2 units
  3. shifts left 2 units
  4. shifts right 2 units
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