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Common Core Standard HSF-BF.A.1b Questions

Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

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Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Find (f+g)(x) if f(x)=4x-3 and g(x)=x+9.
  1. 4x2-27
  2. 4x+6
  3. 5x+6
  4. 5x-6
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Find (f+g)(x), and state its domain, if f(x)=-x2+4x+12 and g(x)=√x+2.
  1. -(x-6)(x+2)32;  x≥-2
  2. -(x-6)(x+2)2;  ℝ
  3. -x2+5x+14;  ℝ
  4. -x2+4x+√x+2+12;  x≥-2
Grade 11 Functions and Relations CCSS: HSF-BF.A.1b
Given f(x)=9x3−6x2+10 and (f+g)(x)=9x3−10x2−10x+5, find g(x).
  1. 9x3−19x2−4x−5
  2. −16x2−10x+15
  3. −4x2−10x−5
  4. 4x2−5
Grade 11 Functions and Relations CCSS: HSF-BF.A.1b
Find (f * g)(x) if f(x) = x - 3 and g(x) = x + 2.
  1. x² + 2x - 6
  2. x² - 6x - 6
  3. x² - x - 6
  4. x² - x + 2
Grade 11 Functions and Relations CCSS: HSF-BF.A.1b
Find (f - g)(x) if f(x) = 3x - 7 and g(x) = x + 4.
  1. 2x - 11
  2. 4x-3
  3. 3x2-x-7
  4. 2x + 11
Grade 11 Function and Algebra Concepts CCSS: HSF-BF.A.1b
Given f(x)=x3−3x2+2 and g(x)=2x2−4x+1, find (f−g)(x).
  1. x3+5x2-4x+1
  2. x3-5x2+4x+1
  3. x3-5x2+4x+3
  4. x3+5x2-2x+1
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
f(x)=-3x-5 and g(x)=4x. Find (f⋅g)(x).
  1. 1x-5
  2. 7x-5
  3. 12x2+20
  4. -12x2-20x
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Find (f-g)(x) if f(x)=7x2-9x+1 and g(x)=-3x2+5x-9.
  1. 4x2-14x+10
  2. 10x2-4x+10
  3. 4x2-4x-8
  4. 10x2-14x+10
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
If f(x)=2x+3 and g(x)=x4x-1, what is (f-g)(x) and its domain?
  1. 2x+34x-1;  x≠14
  2. 8x2+9x-34x-1;  x≠14
  3. x+34x-1;  x≠14
  4. x-2x+4;  x≠2
Grade 11 Functions and Relations CCSS: HSF-BF.A.1b
For f(x)=3x−6 and g(x)=x−2, find f/g(x) and its domain.
  1. 3; all real numbers except x=2
  2. 1; all real numbers
  3. 3; all real numbers
  4. -3; all real numbers except x=3
Grade 11 Functions and Relations CCSS: HSF-BF.A.1b
Given f(x)=x2+2x and g(x)=x+3, find f/g(x) and its domain.
  1. x2+2xx+3 ; all real numbers except x=−3
  2. x2x+3 ; all real numbers except x=0
  3. x2+2x+3x+3 ; all real numbers except x=−3
  4. 3x+2x+3 ; all real numbers
Grade 11 Functions and Relations CCSS: HSF-BF.A.1b
For f(x)=6x+9 and g(x)=x+3, find f/g(x) and its domain.
  1. 6; all real numbers except x=−3x = -3x=−3
  2. 2; all real numbers except x=−2x = -2x=−2
  3. 6xx+3;all real numbers
  4. 6x+9x+3; all real numbers except x=−3
Grade 11 Function and Algebra Concepts CCSS: HSF-BF.A.1b
Let f(x)=5x−7 and g(x)=3x+2. What is (f⋅g)(x)?
  1. 15x2−11x−14
  2. 8x2−5x−5
  3. 15x2+11x−14
  4. 15x2−29x−14
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Find (f⋅g)(x) if f(x)=2x-5 and g(x)=x+3.
  1. 2x2-15
  2. 2x2+x-15
  3. 2x2+11x-15
  4. 2x2-x+15
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
If f(x)=x-2 and g(x)=2x2+4x-70x+7, find (f+g)(x) in its simplest form and its domain.
  1. 2x2+5x-72x+7;  x≠-7
  2. 3x-12;  ℝ
  3. 3x-12;  x≠-7
  4. 3x2+9x+56x+7;  x≠-7
Grade 11 Functions and Relations CCSS: HSF-BF.A.1b
Given f(x) = 5x - 2 and g(x)=x²+3x, what is (f * g)(x)?
  1. 5x³ + 11x² - 6x
  2. 5x³ + 15x² - 2x
  3. 5x² + 3x - 2
  4. x² + 15x - 2
Grade 11 Functions and Relations CCSS: HSF-BF.A.1b
If f(x)=x−2 and g(x)=x2−4xx+2, find (f+g)(x) and its domain.
  1. 2x2-4x-4x+2; x≠−2
  2. 2x−4; x≠−2
  3. x2+4xx+2;x≠2
  4. 2x+4; x≠2
Grade 11 Functions and Relations CCSS: HSF-BF.A.1b
Find (f+g)(x) for f(x)=x−3 and g(x)=x2−9x+3​, and its domain.
  1. x+3; x≠−3
  2. x2+6x−9;R
  3. 2x - 6; x≠−3
  4. x−6; x≠3
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Let f(x)=3x+2andg(x)=7x+6. Find (f⋅g)(x).
  1. 6x2+4x+42
  2. 6x2+4x+56
  3. 21x2+32x+12
  4. 21x2+32x+24
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