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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
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.1, HSF-BF.A.1c
Find (g∘f)(x) and state its domain if f(x)=3x-59x-1 and g(x)=3x+4.
  1. 9x+727x+35,  x≠-2735
  2. 9x+79x-1,  x≠19
  3. 9x+727x+35,  x≠-3527
  4. 45x-199x-1,  x≠19
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Select the possible function rules of f(x) and g(x) if (f∘g)(x)=x2-4. Choose all correct answers.
  1. f(x)=ln(x),  g(x)=ex2-4
  2. f(x)=ln(x2),  g(x)=e12x2-2
  3. f(x)=ln(x2-8),  g(x)=e12x2+2
  4. f(x)=ex-8,  g(x)=ln(x2+4)
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a
A person saves $50 in the first week and increases their savings by $10 each week. Write a recursive function f(x) for the total savings after x weeks.
  1. f(x)=f(x−1)+50,f(1)=10
  2. f(x)=f(x−1)+50,f(1)=50
  3. f(x)=f(x−1)+10,f(1)=10
  4. f(x)=f(x−1)+10,f(1)=50
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a
A student borrows $10,000 with an interest rate of 6% compounded annually. Write an explicit formula for the loan balance, B(t), after t years.
  1. B(t)=10000(1+0.06t)
  2. B(t)=10000(1.06)t
  3. B(t)=10000(1−0.06t)
  4. B(t)=10000(1.06t)
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Given f(x)=x2-4x+6 and g(x)=7x-2, find f(x)+g(x).
  1. x2+3x+4
  2. x2+11x+4
  3. x2+3x+8
  4. x2-3x-8
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.1, HSF-BF.A.1c
If f(x)=x2+3 and g(x)=√x-4 find (f∘g)(x) and state its domain.
  1. x-1,  x≥4
  2. √x2-1,  x<-1orx>1
  3. x+1,  x≥4
  4. x+1, ℝ
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If (f∘g)(x)=2|x+6|, what are possible function rules for f(x) and g(x)? There may be more than one correct answer.
  1. f(x)=√x,  g(x)=4x2+48x+144
  2. f(x)=√x2+6,  g(x)=2x
  3. f(x)=4x2+6,  g(x)=12√x
  4. f(x)=x2+6,  g(x)=2√x
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Let f(x)=1x and g(x)=x2+4. Find (f∘g)(2).
  1. 18
  2. 16
  3. 14
  4. 12
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