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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 [math]1,4,16,64,256,...[/math], which of the following correctly defines this sequence in a recursive form? Assume that [math]n in NN[/math].
  1. [math]t(1) = 1; \ \ t(n) = 4t(n-1), \ n>1[/math]
  2. [math]t(1) = 4; \ \ t(n) = 4t(n-1), \ n>1[/math]
  3. [math]t(1) = 1; \ \ t(n) = 1/4 t(n-1), \ n>1[/math]
  4. [math]t(1) = 1; \ \ t(n) = 2^(2(n-1)), n>1[/math]
Grade 11 Exponents CCSS: HSF-LE.A.2
Given the points (2, 24) and (5, 192), which of the following exponential functions could be created with them? The numerical values in the function have been rounded.
  1. [math]f(x) = 12 • 1.41^x[/math]
  2. [math]f(x) = 6 • 2^x[/math]
  3. [math]f(x) = 8 • 1.5^x[/math]
  4. All of the above
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Find the recursive form of the sequence [math]10, 5, 0, -5, -10,...[/math] Assume [math]n in NN[/math].
  1. [math]t(1) = 10; \ \ t(n) = -t(n-1) + 5, \ n>1[/math]
  2. [math]t(1) = 10; \ \ t(n) = -5 + t(n-1), \ n>1[/math].
  3. [math]t(1) = 10; \ \ t(n) = 10 - t(n-1), \ n>1[/math].
  4. [math]t(1) = 10; \ \ t(n) = t(n-1) - 5, n>1[/math]
Grade 11 Linear Equations CCSS: HSF-LE.A.2
A line passes through the points (0, 7) and (2, 3). What is its linear function?
  1. f(x) = 7x - 2
  2. f(x) = -2x + 3
  3. f(x) = 2x + 7
  4. f(x) = -2x + 7
Grade 11 Exponents CCSS: HSF-LE.A.2
A population of fruit flies doubles every week. If there are 50 flies initially, which function gives the population, P(w), after w weeks?
  1. [math]P(w) = 2(50)^w[/math]
  2. [math]P(w) = 2 + 50w[/math]
  3. [math]P(w) = 50w^2[/math]
  4. [math]P(w) = 50(2)^w[/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 11 Exponents CCSS: HSF-LE.A.2
Create an exponential function from the table of values:
  1. [math]f(x) = 10(3)^x[/math]
  2. [math]f(x) = 30(3)^x[/math]
  3. [math]f(x) = 10(9)^x[/math]
  4. [math]f(x) = 30(1/3)^x[/math]
Grade 11 Quadratic Equations and Expressions CCSS: HSF-LE.A.2
Which equation could describe this graph?
Graph - Quadratic Function y=2x^2
  1. [math]y = 3x^y[/math]
  2. [math]y = x^1/2[/math]
  3. [math]y = 2x^2[/math]
  4. [math]y = 5^2x[/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 9 Linear Equations CCSS: HSF-LE.A.2
Create a linear function, given the points [math](-2,5)[/math] and [math](1,-2)[/math].
  1. [math]f(x) = 7/3 x - 13/3[/math]
  2. [math]f(x) = -3/7 x - 11/7[/math]
  3. [math]f(x) = 3/7 x - 17/7[/math]
  4. [math]f(x) = -7/3 x + 1/3[/math]
Grade 11 Linear Equations CCSS: HSF-LE.A.2
A train is 500 miles from its destination. It travels at 60 miles per hour. Which function models the distance, D(h), after h hours?
  1. D(h) = 500 + 60h
  2. D(h) = 500 - 60h
  3. D(h) = 60 + 500h
  4. [math]D(h) = 500(60)^h[/math]
Grade 11 Exponents CCSS: HSF-LE.A.2
Given the points (0, 8) and (2, 128), which of the following exponential functions could be created with them? The numerical values in the function have been rounded.
  1. [math]f(x) = 2 • 6^x[/math]
  2. [math]f(x) = 16 • 4^x[/math]
  3. [math]f(x) = 10 • 3.5^x[/math]
  4. None of the above
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 9 Linear Equations CCSS: HSF-LE.A.2
Create a linear function from the points [math](-5,4)[/math] and [math](3,4)[/math].
  1. [math]f(x) = 4[/math]
  2. [math]f(x) = 1/9 x + 11/3[/math]
  3. [math]f(x) = -1/9 x + 31/9[/math]
  4. The line that these points define is not a function.
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