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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
Given the equation of graph of y = f(x), if the graph shifts left 2 units, the new equation is__.
  1. y = f(x) + 2
  2. y = f(x) - 2
  3. y = f(x + 2)
  4. y = f(x - 2)
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
g(x)=2tan(x)
Give the equation of the new function, f(x), if g(x) shifted 20° to the left and one unit down.
  1. f(x)=2tan(x+20°)-1
  2. f(x)=2tan(x-20)-1
  3. f(x)=2tan(x+1)-20
  4. f(x)=2tan(90)-20°-1
Grade 11 Trigonometry CCSS: HSF-BF.B.3
On the graph y=sec(x-π4),x∈[-π,π], the vertical asymptotes are located at x=
  1. πand2π
  2. -π2andπ2
  3. -π4and3π4
  4. -3π2and-π4
  5. none of these are correct
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
Is f(x)=1(x+1)(x-1) even, odd, or neither?
  1. Even
  2. Odd
  3. Neither
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
If f(x)=x2 is shifted right by 2 units, what is the new function?
  1. f(x)=(x+2)2
  2. f(x)=(x-2)2
  3. f(x)=x2−2
  4. f(x)=x2+2
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
What transformation is applied to f(x) to get f(x)+5?
  1. Shift left 5 units
  2. Shift right 5 units
  3. Shift up 5 units
  4. Shift down 5 units
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
A function f(x) is odd if:
  1. f(−x) = f(x)
  2. f(−x) = −f(x)
  3. It stretches vertically when multiplied by k
  4. It shifts up when f(x) + k is applied
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
Which most accurately describes how you would transform this function?
f(x)=(x+3)2-4
  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.
Grade 11 Trigonometry CCSS: HSF-BF.B.3
If the base graph of y=cosx was stretched to an amplitude of 4 and a period of 3π, what would be the new function?
  1. y=14cos3x
  2. y=4+cos(32x)
  3. y=cos(3x-4)
  4. y=4cos(23x)
  5. none of these are correct
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
The function f(x)=cos(x³) is_
  1. Even
  2. Odd
  3. Neither
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
The graph of y=ex+2 is shifted:
  1. Left 2 units
  2. Right 2 units
  3. Up 2 units
  4. Down 2 units
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
What transformation occurs when replacing x with x-2 in f(x)?
  1. Shift left 2 units
  2. Shift right 2 units
  3. Vertical stretch by 2
  4. Reflection over y-axis
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
If y = f(x) is transformed to y = (12)f(x), the function__.
  1. Vertically compressed by a factor of 12
  2. Horizontally stretched by a factor of 2
  3. Shifts down 12 units
  4. Reflects over the y-axis
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
A function f(x) is even if:
  1. f(−x) = f(x) (symmetric about the y-axis)
  2. f(−x) = −f(x) (symmetric about the origin)
  3. It shifts left when f(x + k) is applied
  4. It reflects over the x-axis when multiplied by -1
Grade 11 Quadratic Equations and Expressions CCSS: HSF-BF.B.3
What best describes the transformation from f(x)=x2 to f(x)=-(x2)?
  1. Reflect about the x axis
  2. Reflect about the y axis
  3. Stays the same
  4. Moves down 1
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
How is the graph of g(x)=|x+4|-2 related to the parent function f(x)=|x|?
  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 CCSS: HSF-BF.B.3
How does replacing f(x) with f(2x) affect the graph?
  1. Horizontal stretch by 2
  2. Horizontal compression by 1/2​
  3. Vertical stretch by 2
  4. Vertical compression by 1/2
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
For y = |x| - 3, the vertex moves:
  1. Up 3 units
  2. Down 3 units
  3. Left 3 units
  4. Right 3 units
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
The function f(x) = x⁴ - x² is:
  1. Even
  2. Odd
  3. Neither
  4. Both a and b
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