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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 Trigonometry CCSS: HSF-BF.B.3
The period for the function [math]y=-4+2cos(1/3 x-pi)[/math] is equal to which of the following?
  1. [math]pi[/math]
  2. [math]6pi[/math]
  3. [math](9pi)/2[/math]
  4. [math]pi/3[/math]
  5. none of these are correct
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
What is the period of y=cos⁡(3x)?
  1. [math]π[/math]
  2. [math](2π)/3[/math]
  3. [math]3π[/math]
  4. [math]6π[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
For [math]y = f(1/2x)[/math], the graph undergoes:
  1. Horizontal stretch by 2
  2. Horizontal compression by [math]1/2[/math]
  3. Vertical stretch by 2
  4. Vertical compression by [math]1/2[/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 up 2 units
  2. shifts down 2 units
  3. shifts left 2 units
  4. shifts right 2 units
Grade 11 Trigonometry CCSS: HSF-BF.B.3, HSF-TF.B.5
State the amplitude of the function [math]y=1/3cos(x-2)[/math].
  1. [math]1/3[/math]
  2. [math]pi[/math]
  3. [math]-2[/math]
  4. [math]-pi[/math]
  5. none of these are correct
Grade 10 Functions and Relations CCSS: HSF-BF.B.3
Is the function [math]f(x) = e^(-x^2)[/math] even, odd, or neither?
  1. Even
  2. Odd
  3. Neither
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
The function 3f(x-2)+1 involves__.
  1. Right shift, vertical stretch, up shift
  2. Left shift, vertical compression, down shift
  3. Right shift, horizontal stretch, up shift
  4. Left shift, reflection, vertical stretch
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
Which graph represents an even function?
  1. A parabola symmetric about the y-axis
  2. A cubic function symmetric about the origin
  3. A line with slope 1
  4. A square root function
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
The transformation y = -f(x) causes__.
  1. Reflection over y-axis
  2. Reflection over x-axis
  3. Rotation about origin
  4. No change
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
If [math]f(x)=x^2[/math] is shifted right by 2 units, what is the new function?
  1. [math]f(x)=(x+2)^2[/math]
  2. [math]f(x)=(x-2)^2[/math]
  3. [math]f(x)=x^2−2[/math]
  4. [math]f(x)=x^2+2[/math]
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
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