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Common Core Standard HSF-BF.B.3 Questions

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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Grade 11 Functions and Relations CCSS: HSF-BF.B.3
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
Grade 11 Functions and Relations CCSS: HSF-BF.B.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
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
State the amplitude of y=−4sin⁡(x).
  1. 4
  2. -4
  3. [math]π[/math]
  4. [math]2π[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
The period of y = sin(4x) is:
  1. [math] π/2[/math]
  2. [math] π[/math]
  3. [math] 2π[/math]
  4. [math] 4π[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
If y = f(x) is transformed to y = f(x − 3), the function                    .
  1. Shifts up 3 units
  2. Shifts down 3 units
  3. Shifts left 3 units
  4. Shifts right 3 units
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
If y = f(x) is transformed to y = f(4x), the function                                                       .
  1. Vertically stretched by a factor of 4
  2. Horizontally compressed by a factor of [math]1/4[/math]
  3. Shifts right 4 units
  4. Reflects over the y-axis
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
If y = f(x) is transformed to y = 2f(x), the function                     .
  1. shifts up 2 units
  2. shifts right 2 units
  3. becomes "fatter"
  4. becomes "skinnier"
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
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 CCSS: HSF-BF.B.3
What transformations convert f(x) to [math]-1/2f(x+3)[/math]?
  1. Left shift, vertical compression, reflection
  2. Right shift, vertical stretch, reflection
  3. Left shift, horizontal stretch, reflection
  4. Right shift, vertical compression, reflection
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
If y = f(x) is transformed to y = 2f(x), the function                                        .
  1. Vertically stretched by a factor of 2
  2. Horizontally compressed by a factor of 2
  3. Shifts up 2 units
  4. Reflects over the x-axis
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
Is this function even, odd, or neither?
  1. Even
  2. Odd
  3. Neither
  4. Both
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
If y = f(x) is transformed to y = f(x - 2), the function                     .
  1. shifts left 2 units
  2. shifts right 2 units
  3. becomes "fatter"
  4. becomes "skinnier"
Grade 10 Functions and Relations CCSS: HSF-BF.B.3
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]
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
What transformations are applied to f(x) to get 2f(x−1)+3?
  1. Shift right 1, vertical stretch by 2, shift up 3
  2. Shift left 1, vertical compression by 2, shift down 3
  3. Shift right 1, horizontal stretch by 2, shift up 3
  4. Shift left 1, horizontal compression by 2, shift down 3
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
Which function represents a reflection over the y-axis?
  1. -f(x)
  2. f(-x)
  3. f(x)+k
  4. f(kx)
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
If y = f(x) is transformed to y = f(4x), the function                                          .
  1. Vertically stretched by a factor of 4
  2. Horizontally compressed by a factor of 1/4
  3. Shifts right 4 units
  4. Reflects over the y-axis
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