Question

lesson 2 homework practice
function rules
use words and symbols to describe the value of each term as a function of its position. then find the value of the
sixteenth term in the sequence.
1.
position | 2 | 3 | 4 | 5 | n
value of term | 8 | 12 | 16 | 20 |
rule:
16th term:
2.
position | 8 | 9 | 10 | 11 | n
value of term | 14 | 15 | 16 | 17 |
rule:
16th term:
3.
position | 3 | 4 | 5 | 6 | n
value of term | 8 | 10 | 12 | 14 |
rule:
16th term:
4.
position | 2 | 3 | 4 | 5 | n
value of term | 5 | 8 | 11 | 14 |
rule:
16th term:
find a rule for each function table.
5.
input (x) | output (y)
5 | 0
6 | 1
7 | 2
8 | 3
x |
rule:
6.
input (x) | output (y)
2 | 6
3 | 9
4 | 12
5 | 15
x |
rule:
7.
input (x) | output (y)
4 | 5
5 | 7
6 | 9
7 | 11
x |
rule:
8.
input (x) | output (y)
1 | 7
2 | 11
3 | 15
4 | 19
x |
rule:

Explanation:

Step1: Identify sequence pattern (Q4)

Notice term increases by 3. Test: $3(2)-1=5$, matches. Rule: $3n-1$

Step2: Calculate 16th term (Q4)

Substitute $n=16$ into rule.
$\text{16th term}=3(16)-1=47$

Step3: Find input-output rule (Q5)

Output = Input - 5. Rule: $y=x-5$

Step4: Find input-output rule (Q6)

Output = 3×Input. Rule: $y=3x$

Step5: Find input-output rule (Q7)

Test linear rule: $y=2x-3$. $2(4)-3=5$, matches. Rule: $y=2x-3$

Step6: Find input-output rule (Q8)

Test linear rule: $y=4x+3$. $4(1)+3=7$, matches. Rule: $y=4x+3$

Answer:

1. Rule: $\boldsymbol{3n-1}$

16th term: $\boldsymbol{47}$

1. Rule: $\boldsymbol{y=x-5}$
2. Rule: $\boldsymbol{y=3x}$
3. Rule: $\boldsymbol{y=2x-3}$
4. Rule: $\boldsymbol{y=4x+3}$