ANSWER KEYS - Teacher Use Only

Functions | Grade 8

Student Concept Worksheet Answers
1
YES - It is a function
Each x-value (2, 4, 6, 8) appears only once, each with one y-value.
2
a) f(3) = 14 | b) f(0) = 2 | c) f(-2) = -6
f(x) = 4x + 2: f(3) = 4(3)+2 = 14, f(0) = 4(0)+2 = 2, f(-2) = 4(-2)+2 = -6
3
NO - Not a function
x = 2 appears twice with different y-values (5 and 7). Each input must have exactly one output.
4
a) Non-linear | b) Linear | c) Non-linear
x² and 2/x are non-linear. Only 5x - 3 is in y = mx + b form.
Practice Worksheet Answers

Part A: Identifying Functions

#AnswerExplanation
1YESEach x-value is unique
2NOx = 3 appears twice with y = 2 and y = 6
3YESEach x is unique (different y's for different x's is OK)
4NOx = 1 has y = 3 AND y = 5; x = 2 has y = 7 AND y = 9

Part B: Evaluating Functions

5
a) 13 | b) 7 | c) -1 | d) 27
f(x) = 2x+7: f(3)=13, f(0)=7, f(-4)=-1, f(10)=27
6
a) 1 | b) 22 | c) 6 | d) -3
g(x) = x²-3: g(2)=1, g(5)=22, g(-3)=6, g(0)=-3
7
a) 4 | b) 13 | c) -2
h(x) = -3x+10: h(2)=4, h(-1)=13, h(4)=-2
8
x = 4
5x - 1 = 19 → 5x = 20 → x = 4

Part C: Linear or Non-Linear

#FunctionAnswer
9f(x) = 3x - 8Linear
10g(x) = x² + 2xNon-linear
11h(x) = 4/xNon-linear
12f(x) = -5xLinear

Part D: Ordered Pairs

#AnswerExplanation
13YESEach x is unique (1,2,3,4,5)
14YESSame y is OK! Different x's can have same y
15NOx = 3 appears 4 times with different y's

Part E: Real-World

16
a) Cost for 5-mile ride | b) $13 | c) 6 miles
f(5) = 2(5)+3 = $13. For f(m) = 15: 2m+3 = 15, m = 6
17
a) Non-linear | b) 36 | c) 36
h(t) has t², so non-linear. h(1)=-16+48+4=36, h(2)=-64+96+4=36
18
YES, outputs can repeat
Example: f(x) = x² gives f(2)=4 and f(-2)=4. Same output, different inputs - still a function!
19
b = 5
f(3) = 2(3) + b = 11 → 6 + b = 11 → b = 5
FAST Practice Quiz Answers
1
A) Table A only
Table A: all x unique. Table B: x=1 gives y=4 AND y=7.
2
A) 7
f(4) = 3(4) - 5 = 12 - 5 = 7
3
C) f(x) = x² - 1
x² makes it non-linear. Others are all linear (y = mx + b form).
4
Select: {(1,2),(2,4),(3,6)} and {(2,5),(3,5),(4,5)}
{(1,2),(2,4),(3,6)} - all x unique ✓
{(5,3),(5,7),(6,8)} - x=5 has two y's ✗
{(2,5),(3,5),(4,5)} - same y is OK ✓
{(1,1),(2,2),(1,3)} - x=1 has two y's ✗
5
B) The graph represents a function
Vertical line test determines if a relation is a function, not if it's linear.
6
B) x = 6
2x + 8 = 20 → 2x = 12 → x = 6
Scoring Guide
ScoreInterpretationRecommended Action
6/6MasteryReady for graphing functions and transformations.
4-5/6ApproachingReview specific weak area (notation, identification, or linear/non-linear).
2-3/6DevelopingReteach using function machines. Focus on "one input = one output" rule.
0-1/6InterventionStart with concrete examples. Use input-output tables before graphs.
FAST Success Kit | Grade 8 | FL B.E.S.T. Standards: MA.8.AR.5.1, MA.8.AR.5.2, MA.8.AR.5.3 | Answer Key - Teacher Use Only