Building Functions Test Answer Key with Scoring – Algebra 1

Question 1 Plumber Rates (2 points)

1. C(h) = 65 + 48h.
2. 65 + 48(2.5) = 65 + 120 = $185.

Scoring: 1 point per part.

Question 2 Recursive to Explicit (2 points)

Each step subtracts 35, so A(n) = 500 − 35n.

A(8) = 500 − 280 = 220.

Scoring: 1 point for the explicit rule, 1 point for A(8).

Question 3 Linear Table (2 points)

Rates: (20 − 11) ÷ 3 = 3 and (32 − 20) ÷ 4 = 3, a constant rate of 3 per unit.

Then 11 = 3(2) + b gives b = 5. y = 3x + 5.

Scoring: 1 point for showing the constant rate, 1 point for the rule.

Question 4 Combine Two Functions (3 points)

1. 2x² − x + 5x + 3 = 2x² + 4x + 3.
2. 2x² − x − 5x − 3 = 2x² − 6x − 3.
3. f(−1) = 3 and g(−1) = −2, so the product is −6.

Scoring: 1 point per part.

Question 5 Break-Even for a Bake Sale (3 points)

1. P(x) = 22x − (300 + 10x) = 12x − 300.
2. 12x − 300 = 0 gives x = 25.
3. P(40) = 480 − 300 = $180.

Scoring: 1 point per part.

Question 6 Inverse of a Linear Function (3 points)

1. y = 5x − 8, so x = y + 85. f⁻¹(x) = x + 85.
2. f(3) = 7 and f⁻¹(7) = 155 = 3 ✓.

Scoring: (a) 1 point for solving for x, 1 point for the inverse. (b) 1 point.

Question 7 Rental Hours (3 points)

1. R = 8h + 15, so h = R − 158. h = R − 158.
2. 63 − 158 = 488 = 6 hours.

Scoring: (a) 1 point for solving, 1 point for the function. (b) 1 point.

Question 8 Candle Height (2 points)

1. The height changes by the same amount, −0.75 inch, every hour, a constant rate per unit interval. The slope means the candle shortens 0.75 inch each hour.
2. 14 − 0.75(6) = 14 − 4.5 = 9.5 inches.

Scoring: 1 point per part.