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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.1b
Given [math]f(x)=3x+4 and g(x)=2x-3 [/math], find [math]f(x) *g(x)[/math].
  1. [math]6x^2+x-12[/math]
  2. [math]6x^2-x+12[/math]
  3. [math]-6x^2-x-12[/math]
  4. [math]6x^2-x-12[/math]
Grade 11 Functions and Relations CCSS: HSF-IF.A.1, HSF-BF.A.1, HSF-BF.A.1c
Find the domain of the composite function [math]f(g(x))[/math].

[math]f(x)= x+3[/math]
[math]g(x)= 2/(x+6)[/math]
  1. [math](-oo,3) uu (3,oo)[/math]
  2. [math](-oo,oo)[/math]
  3. [math](-oo,-6) uu (-6,3) uu (3,oo)[/math]
  4. [math](-oo,-6) uu (-6,oo)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Let [math]f(x) = 5x-2 and g(x)= (3x)/ (2+x) [/math]. Find [math](g@f)(x)[/math].
  1. [math](15x)/(x+2) - 2[/math]
  2. [math](15x)/(2+5x)[/math]
  3. [math] (3x(5x-2))/(x+2)[/math]
  4. [math](15x-6)/(5x)[/math]
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Given the sequence [math]128, 64, 32, 16, 8, ...[/math] which of the following functions describes it? Assume [math]n in NN[/math].
  1. [math]t(1) = 128; \ \ t(n) = 2 t(n-1), \ n>1[/math]
  2. [math]t(1) = 128; \ \ t(n) = 128 - t(n-1), \ n>1[/math]
  3. [math]t(1) = 128; \ \ t(n) = t(n) - 1/2t(n-1), n>1[/math]
  4. [math]t(1) = 128; \ \ t(n) = 1/2 t(n-1), \ n>1[/math]
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Find [math](f*g)(x)[/math] if [math]f(x) = x^2 - 6x + 2[/math] and [math]g(x) = 5x-7[/math].
  1. [math]5x^3 +23x^2 -32x - 14[/math]
  2. [math]5x^3 - 37x^2 + 52x - 14[/math]
  3. [math]5x^3 - 6x - 14[/math]
  4. [math]-32x^2 + 42x - 14[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find [math](f@g)(x)[/math] and state its domain, if [math]f(x) = log(-x-5)[/math] and [math]g(x) = sqrt(x)[/math].
  1. [math]log(-sqrt(x)-5), \ \ x>0[/math]
  2. [math]log(-sqrt(x)-5), \ \ x<0[/math]
  3. [math]log(-sqrt(x)-5), \ \ x>25[/math]
  4. This composite function is not possible.
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
[math]f(x) = sqrt(x+3)[/math] and [math]g(x)=2x[/math]. Find [math](f @ g)(4)[/math].
  1. [math]2sqrt14[/math]
  2. [math]sqrt11[/math]
  3. [math]sqrt14[/math]
  4. [math]2sqrt7[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Let [math]f(x) = 3x^2-5x and g(x)=sqrt(x+2)[/math]. Find [math](g@f)(x)[/math].
  1. [math]3(x+2) - 5sqrt(x+2)[/math]
  2. [math]sqrt(3x^2-5x+2[/math]
  3. [math]-2x + 6[/math]
  4. [math]sqrt(3)x - (sqrt(5) -1) sqrt(x)[/math]
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Which of the following functions describes the sequence [math]18, 31/2, 13, 21/2, 8, ... ?[/math] Assume that [math]n in NN[/math].
  1. [math] t(1) = 18; \ \ t(n) = 43/50 t(n-1), n>1[/math]
  2. [math]t(1) = 18; \ \ t(n) = t(n-1) - 5/2, n>1[/math]
  3. [math]t(1) = 18; \ \ t(n) = t(n-2) - 5, n>2[/math]
  4. [math]t(1) = 18; \ \ t(n) = 5/2 - t(n-1), t>1[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
For [math]f(x) = 7x^3 - 8x^2 + x - 12[/math] and [math]g(x) = -x^2 + 5x +2[/math], find [math](f+g)(x)[/math].
  1. [math]7x^3 - 7x^2 - 4x - 14[/math]
  2. [math]7x^3 - 8x^2 + 5x - 12[/math]
  3. [math]7x^3 + 9x^2 + x - 10[/math]
  4. [math]7x^3 - 9x^2 + 6x - 10[/math]
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If [math](f@g)(x) = x^2 + 2x + 4[/math], which of the following could be the functions [math]f(x)[/math] and [math]g(x) ?[/math] Choose all correct answers.
  1. [math]f(x) = x^2 + 3, \ \ g(x) = x+1[/math]
  2. [math]f(x) = x + 2, \ \ g(x) = x^2 + 2x + 2[/math]
  3. [math]f(x) = x - 5, \ \ g(x) = x^2 + 2x + 9[/math]
  4. [math]f(x) = x^2 + 2, \ \ g(x) = 2x[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
[math]g(x)= 8x^2-3[/math] and [math]f(x)= -4x^2[/math].
Find [math] (g + f) (x) [/math].
  1. [math]-32x^4-3[/math]
  2. [math]12x^4 - 3[/math]
  3. [math]4x^2 -3[/math]
  4. [math]4x^4 -3[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
[math]f(x) =7x+9 and g(x) = 4x-1[/math]. Find [math](f @ g)(x)[/math].
  1. [math]28x+8[/math]
  2. [math]28x+16[/math]
  3. [math]28x+2[/math]
  4. [math]28x+35[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If [math] g(x) = 4/(2-x) and (g@f)(x) = -2/x^2[/math], find [math]f(x)[/math].
  1. [math](2x^2)/(x^2+1)[/math]
  2. [math](x-2)/x^2[/math]
  3. [math]2x^2 + 2[/math]
  4. [math]-1/(2(x^2 - 2))[/math]
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2
Which of the following functions correctly describes the sequence [math]1,3,5,9,13,21,...?[/math] Assume that [math]n in NN[/math].
  1. [math] t(1) = 1, t(2) = 3; \ \ t(n) = 2t(n-2) + 3, n>2[/math]
  2. [math]t(1) = 1; \ \ t(n) = t(n-1) + 2, n>1[/math]
  3. [math]t(1)=1, t(2)=3; \ \ t(n) = t(n-2) + t(n-1) + 1, n>2[/math]
  4. [math]t(1) = 1; \ \ t(n) = t(n-1) + 2^(n-1), \ n>1[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Find [math](f+g)(x)[/math] if [math]f(x) = 3x^2 - 9[/math] and [math]g(x) = -7x + 1[/math].
  1. [math]3x^2 - 7x - 8[/math]
  2. [math]3x^2 - 8[/math]
  3. [math]3x^2 + 7x - 10[/math]
  4. [math]-4x^2 - 8[/math]
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