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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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Which formula represents the general term of the following sequence? $1/2, -1, 2, -4, ...$
1. $a_n = 1/2 * 2^n$
2. $a_n = 1/2 * (-2)*(n-1)$
3. $a_n = 1/2 * -2^(n-1)$
4. $a_n = 1/2 * (-2)^(n-1)$
Which recursive function defines the sequence $0, 2, 2, 10, 18, 58, 130, ...$ for $n in N ?$
1. $t(1) = 0; \ \ t(n) = t(n-1) + n-2, \ n>1$
2. $t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 4t(n-2), \ n>2$
3. $t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 2t(n-2), \ n>2$
4. $t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 4(n-2), \ n>2$
Which of the following recursive functions defines the sequence $5,8,11,14,... ?$ Assume $n in NN$.
1. $t(1) = 3; \ \ t(n) = t(n-1) + 5, \ n>1$
2. $t(1) = 5, \ \ t(n) = t(n-1) - 3, \ n>1$
3. $t(1) = 5, \ \ t(n) = t(n-1) + 3, \ n>1$
4. $t(2) = 8, \ \ t(n) = t(n-2) + 6, \ n>2$
Given the sequence $1,4,16,64,256,...$, which of the following correctly defines this sequence in a recursive form? Assume that $n in NN$.
1. $t(1) = 1; \ \ t(n) = 4t(n-1), \ n>1$
2. $t(1) = 4; \ \ t(n) = 4t(n-1), \ n>1$
3. $t(1) = 1; \ \ t(n) = 1/4 t(n-1), \ n>1$
4. $t(1) = 1; \ \ t(n) = 2^(2(n-1)), n>1$
Find the recursive form of the sequence $10, 5, 0, -5, -10,...$ Assume $n in NN$.
1. $t(1) = 10; \ \ t(n) = -t(n-1) + 5, \ n>1$
2. $t(1) = 10; \ \ t(n) = -5 + t(n-1), \ n>1$.
3. $t(1) = 10; \ \ t(n) = 10 - t(n-1), \ n>1$.
4. $t(1) = 10; \ \ t(n) = t(n-1) - 5, n>1$
Given the sequence $128, 64, 32, 16, 8, ...$ which of the following functions describes it? Assume $n in NN$.
1. $t(1) = 128; \ \ t(n) = 2 t(n-1), \ n>1$
2. $t(1) = 128; \ \ t(n) = 128 - t(n-1), \ n>1$
3. $t(1) = 128; \ \ t(n) = t(n) - 1/2t(n-1), n>1$
4. $t(1) = 128; \ \ t(n) = 1/2 t(n-1), \ n>1$
Which of the following functions describes the sequence $18, 31/2, 13, 21/2, 8, ... ?$ Assume that $n in NN$.
1. $t(1) = 18; \ \ t(n) = 43/50 t(n-1), n>1$
2. $t(1) = 18; \ \ t(n) = t(n-1) - 5/2, n>1$
3. $t(1) = 18; \ \ t(n) = t(n-2) - 5, n>2$
4. $t(1) = 18; \ \ t(n) = 5/2 - t(n-1), t>1$
Grade 9 Linear Equations CCSS: HSF-LE.A.2
Create a linear function, given the points $(-2,5)$ and $(1,-2)$.
1. $f(x) = 7/3 x - 13/3$
2. $f(x) = -3/7 x - 11/7$
3. $f(x) = 3/7 x - 17/7$
4. $f(x) = -7/3 x + 1/3$
Which of the following functions correctly describes the sequence $1,3,5,9,13,21,...?$ Assume that $n in NN$.
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. $t(1) = 1; \ \ t(n) = t(n-1) + 2^(n-1), \ n>1$