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Common Core Standard HSF-BF.A.1 Questions

Write a function that describes a relationship between two quantities.

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Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
[math]f(x) = sqrt(x+8) and g(x)= 8x-12[/math]. Find [math](f @ g)(x)[/math].
  1. [math]2sqrt(2x-1)[/math]
  2. [math]8sqrt(x+8)-12[/math]
  3. [math]8sqrt(x-4)[/math]
  4. [math]2sqrt(2x+1)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
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 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2
Given the sequence [math]1, -3, -9, -17, -27, ...[/math], which of the following functions correctly describes it? Assume that [math]n in NN[/math].
  1. [math]t(1) = 1, t(2) = -3; \ \ t(n) = t(n-1) - 6t(n-2), n>2[/math]
  2. [math]t(1) = 1; \ \ t(n) = t(n-1) -4, \ n>1[/math]
  3. [math]t(1) = 1; \ \ t(n) = t(n-1) - 2n, \ n > 1[/math]
  4. [math]t(1) = 1; \ \ t(n) = (-1)^(n-1) * 3 * t(n-1), n>1[/math]
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Find [math]f(x)[/math] if [math]g(x) = 3x-1[/math] and [math](f*g)(x) = 6x^2 + 10x - 4[/math].
  1. [math]f(x) = x-2[/math]
  2. [math]f(x) = 2x + 10/3[/math]
  3. [math]f(x) = x+2[/math]
  4. [math]f(x) = 2x+4[/math]
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If [math](f@g)(x) = 10x - 2[/math], which of the following are possible function rules for [math]f(x)[/math] and [math]g(x) ?[/math] Choose all correct answers.
  1. [math]f(x) = 10x + 10, \ \ g(x) = x - 12[/math]
  2. [math]f(x) = 2x-4, \ \ g(x) = 5x+1[/math]
  3. [math]f(x) = 8x-9, \ \ g(x) = 5/4 x - 11/4[/math]
  4. [math]f(x) = 1/2x - 3 \ \ g(x) = 20x + 2[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a
An investment of $1,000 grows by 5% each year. Write a recursive rule for the total value, [math]V_n[/math]​, after n years.
  1. [math]V_n=1.05V_(n-1),V_0=0[/math]
  2. [math]V_n=1.05V_(n-1),V_0=1000[/math]
  3. [math]V_n=V_(n-1)+0.05,V_0=1000[/math]
  4. [math]V_n=1.5V_(n-1),V_0=1000[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
[math]f(x) = 3x-12 and g(x) = 4x[/math]. Find [math](f @ g)(x)[/math].
  1. [math]12x^2+48x[/math]
  2. [math]12x-48[/math]
  3. [math]12x-12[/math]
  4. [math]7x-12[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Let [math]f(x)=3x +2 and g(x)=7x +6[/math]. Find [math](f*g)(x)[/math].
  1. [math]6x^2 +4x +42[/math]
  2. [math]6x^2 +4x +56[/math]
  3. [math]21x^2 +32x +12[/math]
  4. [math]21 x^2 + 32x +24[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
If [math]f(x) = 9x^3 - 6x^2 + 10[/math] and [math](f+g)(x) = 9x^3 - 10x^2 - 10x + 5[/math], find [math]g(x)[/math].
  1. [math]9x^3 - 19x^2 - 4x - 5[/math]
  2. [math]-16x^2 -10x +15[/math]
  3. [math]-4x^2 - 10x - 5[/math]
  4. [math]4x^2 - 5[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
For [math](f@g)(x) = e^(-x^2 + 6)[/math], which of the following are possible function rules of [math]f(x)[/math] and [math]g(x) ?[/math] There may be more than one correct answer.
  1. [math]f(x) = e^x, \ \ g(x) = -x^2 + 6[/math]
  2. [math]f(x) = e^(-x+6), \ \ g(x) = x^2[/math]
  3. [math]f(x) = e^(-x^2 - 4x + 2), \ \ g(x) = x-2[/math]
  4. [math]f(x) = x^2, \ \ g(x) = e^(-1/2x^2 + 3)[/math]
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