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Common Core Standard HSF-LE.A.2 Questions

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

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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 128,64,32,16,8,... which of the following functions describes it? Assume n∈ℕ.
  1. t(1)=128;  t(n)=2t(n-1), n>1
  2. t(1)=128;  t(n)=128-t(n-1), n>1
  3. t(1)=128;  t(n)=t(n)-12t(n-1),n>1
  4. t(1)=128;  t(n)=12t(n-1), n>1
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 18,312,13,212,8,...? Assume that n∈ℕ.
  1. t(1)=18;  t(n)=4350t(n-1),n>1
  2. t(1)=18;  t(n)=t(n-1)-52,n>1
  3. t(1)=18;  t(n)=t(n-2)-5,n>2
  4. t(1)=18;  t(n)=52-t(n-1),t>1
Grade 9 Linear Equations CCSS: HSF-LE.A.2
Create a linear function, given the points (-2,5) and (1,-2).
  1. f(x)=73x-133
  2. f(x)=-37x-117
  3. f(x)=37x-177
  4. f(x)=-73x+13
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 1,3,5,9,13,21,...? Assume that n∈ℕ.
  1. t(1)=1,t(2)=3;  t(n)=2t(n-2)+3,n>2
  2. t(1)=1;  t(n)=t(n-1)+2,n>1
  3. t(1)=1,t(2)=3;  t(n)=t(n-2)+t(n-1)+1,n>2
  4. t(1)=1;  t(n)=t(n-1)+2n-1, n>1
Grade 9 Linear Equations CCSS: HSF-LE.A.2
Create a linear function from the points (-5,4) and (3,4).
  1. f(x)=4
  2. f(x)=19x+113
  3. f(x)=-19x+319
  4. The line that these points define is not a function.
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 correctly describe(s) the sequence 3,5,7,9,11,...? Assume that n∈ℕ. There may be more than one correct answer.
  1. t(1)=3;  t(n)=t(n-1)+2, n>1
  2. t(1)=3, t(2)=5;  t(n)=t(n-2)+4,n>2
  3. t(1)=3, t(2)=5;  t(n)=-t(n-1)+2t(n-2)+6, n>2
  4. t(1)=3;  t(n+1)=t(n)+2, n≥1
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2
Given the sequence 1,-3,-9,-17,-27,..., which of the following functions correctly describes it? Assume that n∈ℕ.
  1. t(1)=1,t(2)=-3;  t(n)=t(n-1)-6t(n-2),n>2
  2. t(1)=1;  t(n)=t(n-1)-4, n>1
  3. t(1)=1;  t(n)=t(n-1)-2n, n>1
  4. t(1)=1;  t(n)=(-1)n-1⋅3⋅t(n-1),n>1
Grade 9 Functions and Relations CCSS: HSF-LE.A.2
What is the equation of the linear function in the graph? Assume the horizontal axis represents x and the vertical axis f(x).
Graph - Linear Function y=-2x
  1. f(x)=-x
  2. f(x)=-2x
  3. f(x)=-12x
  4. f(x)=12x
Grade 11 Functions and Relations CCSS: HSF-LE.A.2

This question is a part of a group with common instructions. View group »

Given the information in the previous two questions and properties of both functions, choose which of the following statements is definitely true.
  1. f(x)>p(x) for x≥2524, since the steady percent increase of f(x) means it will grow by ever greater amounts over a one unit interval. Although the amount that p(x) increases over a one unit interval will also grow, it will do so more slowly.
  2. f(x)>p(x) may be true for all values of x greater than or equal to 2524, or it may only be greater for some interval before p(x) becomes greater. Since the percent increase of p(x) is always changing, it cannot be certain which function will be greater.
  3. f(x)>p(x) for 2524≤x<x0, where x0 is some real value of x greater than 2524. Because f(x) is only increasing by 1% each unit interval, the amount it increases over a one unit interval will eventually slow down, and p(x) will become larger.
  4. f(x) will be equal to p(x) for exactly one more value of x for x>2524. Let this point be x0. It cannot be determined with the information given which function will be greater for x>x0.
Grade 10 Sequences and Series CCSS: HSF-IF.A.3, HSF-BF.A.2, HSF-LE.A.2
What is the recursive function of the geometric sequence 3, 4.5, 6.75...?
  1. f(n)=1.5f(n-1) where f(1)=3
  2. f(n)=3×1.5n-1
  3. f(n)=1.5×3n-1
  4. f(n)=3f(n-1) where f(1)=1.5
Grade 10 Sequences and Series CCSS: HSF-IF.A.3, HSF-BF.A.2, HSF-LE.A.2
What is the explicit function of the geometric sequence 3, 4.5, 6.75, ...?
  1. f(n)=1.5f(n-1) where f(1)=3
  2. f(n)=3⋅1.5n-1
  3. f(n)=1.5⋅3n-1
  4. f(n)=3f(n-1) where f(1)=1.5
Grade 11 Quadratic Equations and Expressions CCSS: HSF-LE.A.2
Which equation could describe this graph?
  1. y=(x-1)(x-8)
  2. y=(x-4)(x+2)
  3. y=(x-2)(x+4)
  4. y=(x+1)(x+8.5)
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