Functions Test Answer Key with Scoring – Grade 8

Question 1 Function or not? (2 points)

1. The input 6 has two outputs, 13 and 15: not a function.
2. Each input appears once; the repeated output 4 is allowed: a function.

(a) not a function (b) function

Scoring: 1 point per part, with a reason.

Question 2 Evaluate (2 points)

f(−2) = 3(4) − 5 = 7. f(4) = 3(16) − 5 = 43.

f(−2) = 7 and f(4) = 43

Scoring: 1 point each.

Question 3 Which graph? (3 points)

1. Graph A.
2. Any vertical line meets Graph A once. A vertical line such as x = 4 meets Graph B twice.
3. For example (4, 2) and (4, −2).

(a) Graph A (b) Graph B fails the test (c) (4, 2) and (4, −2)

Scoring: 1 point per part.

Question 4 Compare two functions (3 points)

1. Function 1: 4. Function 2: 2 (the outputs rise by 2).
2. Function 1: 3. Function 2: 6.
3. Function 1 gives 4(10) + 3 = 43. Function 2 gives 2(10) + 6 = 26.

(a) 4 and 2 (b) 3 and 6 (c) Function 1

Scoring: 1 point per part.

Question 5 Linear or not? (3 points)

1. The changes are 4, 6 and 8.
2. The rate of change is not constant, so it is nonlinear.
3. The outputs rise by 3 and start at 5: y = 3x + 5.

(a) 4, 6, 8 (b) nonlinear (c) y = 3x + 5

Scoring: 1 point per part.

Question 6 Graph and equation (3 points)

1. Rate (11 − 3) ÷ 4 = 2; initial value 3.
2. The equation has rate 2.5, which is more than 2, so it changes faster.
3. y = 2x + 3.

(a) 2 and 3 (b) the equation (c) y = 2x + 3

Scoring: 1 point per part.

Question 7 Rising water (2 points)

d(4) = 5(4) + 8 = 28. For 43: 5t + 8 = 43, so 5t = 35 and t = 7.

28 inches; 7 hours

Scoring: 1 point each.

Question 8 Is area linear? (2 points)

The areas are 1, 4 and 9. The change from side 1 to 2 is 3, and from side 2 to 3 is 5. The rate of change is not constant, so the function is nonlinear.

Rates 3 and 5 differ: not linear

Scoring: 1 point for the areas and changes, 1 point for the conclusion.