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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 9 Logarithms CCSS: HSF-BF.B.3
Write the equation of a logarithmic function that is reflected over the x-axis and translated two units to the left and three units above the parent function [math]f(x)=lnx[/math].
  1. [math]g(x)=3-ln(x)+2[/math]
  2. [math]g(x)=3+ln(x)-2[/math]
  3. [math]g(x)=3-ln(x+2)[/math]
  4. [math]g(x)=-3+ln(x-2)[/math]
Grade 11 Trigonometry CCSS: HSF-BF.B.3
If [math]y=-3tan(2x)[/math], then the base function is being
  1. compressed vertically and stretched horizontally.
  2. stretched vertically, stretched horizontally, and reflected over the x-axis.
  3. stretched vertically, compressed horizontally, and shifted down.
  4. stretched vertically, compressed horizontally, and reflected over the x-axis.
  5. none of these are correct
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
[math]g(x)= 2tan(x)[/math]
Give the equation of the new function, f(x), if g(x) shifted 20° to the left and one unit down.
  1. [math]f(x)=2tan(x+20deg)-1[/math]
  2. [math]f(x)=2tan(x-20)-1[/math]
  3. [math]f(x)=2tan(x+1)-20[/math]
  4. [math]f(x)=2tan(90)-20deg-1[/math]
Grade 11 Trigonometry CCSS: HSF-BF.B.3
On the graph [math]y=sec (x-pi/4), x in [-pi,pi][/math], the vertical asymptotes are located at [math]x=[/math]
  1. [math]pi and 2pi[/math]
  2. [math]-pi/2 and pi/2[/math]
  3. [math]-pi/4 and (3pi)/4[/math]
  4. [math]-(3pi)/2 and -pi/4[/math]
  5. none of these are correct
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
Is [math]f(x) = 1 / ((x+1)(x-1)) [/math] even, odd, or neither?
  1. Even
  2. Odd
  3. Neither
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
Which most accurately describes how you would transform this function?
[math]f(x)=(x+3)^2-4[/math]
  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 [math]y=cosx[/math] was stretched to an amplitude of 4 and a period of [math]3pi[/math], what would be the new function?
  1. [math]y=1/4 cos 3x[/math]
  2. [math]y=4+cos (3/2 x)[/math]
  3. [math]y=cos (3x-4)[/math]
  4. [math]y=4cos(2/3 x)[/math]
  5. none of these are correct
Grade 11 Quadratic Equations and Expressions CCSS: HSF-BF.B.3
What best describes the transformation from [math] f(x) = x^2 [/math] to [math]f(x)=-(x^2)[/math]?
  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 [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 CCSS: HSF-BF.B.3
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 CCSS: HSF-BF.B.3
Which of the following could identify the transformation of a parabola with a vertex of (-4,-6) to a parabola with a vertex of (1,-6)?
  1. [math]f(x)+5[/math]
  2. [math]5f(x)[/math]
  3. [math]f(x+5)[/math]
  4. [math]f(x-5)[/math]
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 right 2 units
  2. shifts down 2 units
  3. shifts left 2 units
  4. shifts up 2 units
Grade 10 Quadratic Equations and Expressions CCSS: HSF-BF.B.3
Which option best describes the transformations of the graph of the function [math]y=2(x-1)^2[/math] from the parent function?
  1. Move up one and stretch vertically
  2. Move up one and compress vertically
  3. Move right one and stretch vertically
  4. Move down one and compress vertically
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
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
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