This grade 8 functions test answer key gives the full solution and the scoring guide for each of the 9 test questions on introduction to functions.
Use this key to score the test out of 20 points. Each solution gives a model answer, and the scoring note explains how partial credit is awarded. Accept equivalent explanations in the student’s own words, such as one output for every input, as long as the reasoning is correct.
Grade 8 Functions Test Answer Key: questions 1–5
Question 1: Mapping diagram (2 points)
Each input (2, 4 and 6) has exactly one output. Two inputs sharing the output 5 is allowed.
Yes, it is a function.
Scoring: 1 point for the correct answer; 1 point for a valid reason about one output per input.
Question 2: Table of values (2 points)
The input 3 has outputs 6 and 8.
No, it is not a function, because one input has two different outputs.
Scoring: 1 point for the answer; 1 point for naming input 3 with outputs 6 and 8.
Question 3: Evaluate (2 points)
\(f(-2)=-3(-2)+5=11\) and \(f(4)=-3(4)+5=-7\).
\(f(-2)=11\), \(f(4)=-7\).
Scoring: 1 point for each correct value.
Question 4: Write an equation (2 points)
The outputs rise by 4, so \(m=4\). Then \(4(1)+b=5\) gives \(b=1\).
\(y=4x+1\).
Scoring: 1 point for the rate 4; 1 point for the full equation.
Question 5: Points on a line (3 points)
- The points rise 2 for each 1 to the right, a constant change, so it is linear.
- The rate of change is 2.
- The graph crosses the y-axis at 1: \(y=2x+1\).
Scoring: 1 point per part.
Grade 8 Functions Test Answer Key: questions 6–9
Question 6: Linear or nonlinear? (3 points)
- It has the form \(y=mx+b\): linear.
- Sides 1, 2, 3 give areas 1, 4, 9; the change is not constant: nonlinear.
- The outputs rise by 3, 5, 7: nonlinear.
Scoring: 1 point per part.
Question 7: Compare two functions (2 points)
A: rate 5, initial value 2. B: rate \(\frac{9-1}{2-0}=4\), initial value 1.
A has the greater rate (5 versus 4) and the greater initial value (2 versus 1).
Scoring: 1 point for the rates compared; 1 point for the initial values compared.
Question 8: Taxi fare (2 points)
\(f(7)=2(7)+3=17\), so the fare is $17.
\(2m+3=25\) gives \(2m=22\) and \(m=11\), so 11 miles.
Scoring: 1 point for each answer.
Question 9: Area graph (2 points)
The areas 1, 4, 9, 16 increase by 3, 5 and 7, so the rate of change is not constant. The points do not lie on a line.
The function is nonlinear.
Scoring: 1 point for the answer; 1 point for a correct justification.
Scoring summary
20 points: add the points of every question of this grade 8 functions test answer key.
How to use this grade 8 functions test answer key
Use this grade 8 functions test answer key to score the test fairly and to see which skills need more practice.
See every chapter on the Grade 8 math page.
