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.
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.
20 points
See every chapter on the Grade 8 math page.