1. We are asked to express the relationship between time spent on a job and the fee charged by a carpenter. 2. Let $t$ be the time in hours and $F(t)$ be the fee charged in euros. 3. The carpenter charges a flat fee of 40 euros plus 30 euros per hour, so the function is: $$F(t) = 30t + 40$$ 4. Domain: Since the carpenter cannot work negative hours, $t \geq 0$. So domain is $[0, \infty)$. 5. Range: The smallest fee is when $t=0$, fee is 40 euros, and it increases without bound, so range is $[40, \infty)$. 6. This relation is a function because for each input $t$ (time), there is exactly one output $F(t)$ (fee). --- 1. Express the relationship between time elapsed since the drain plug was pulled and the amount of water left. 2. Let $t$ be time in minutes since the plug was pulled, and $W(t)$ the amount of water in liters. 3. Initial water is 120 liters and water drains at 25 liters per minute, so: $$W(t) = 120 - 25t$$ 4. Domain: The water cannot be negative, so $W(t) \geq 0 \Rightarrow 120 - 25t \geq 0 \Rightarrow t \leq 4.8$. Also, $t \geq 0$, so domain is $[0, 4.8]$. 5. Range: At $t=0$, $W=120$ liters. At $t=4.8$, $W=0$ liters. So range is $[0, 120]$. 6. This relation is a function because each time $t$ corresponds to exactly one water amount $W(t)$. --- 1. Express the relationship between size of a land parcel and final price including taxes. 2. Let $x$ be size in square meters and $P(x)$ be the final price. 3. Cost before tax is $200x$. Taxes add 15%, so final price is: $$P(x) = 200x + 0.15(200x) = 200x(1 + 0.15) = 230x$$ 4. Domain: Size $x$ cannot be negative, so $x \geq 0$. 5. Range: Price $P(x)$ is at least 0 and increases as $x$ increases, so range is $[0, \infty)$. 6. This is a function because each parcel size determines exactly one price. Final answers: 1. $F(t) = 30t + 40$, domain $t \geq 0$, range $F(t) \geq 40$. 2. $W(t) = 120 - 25t$, domain $0 \leq t \leq 4.8$, range $0 \leq W(t) \leq 120$. 3. $P(x) = 230x$, domain $x \geq 0$, range $P(x) \geq 0$. Each relation is a function because each input maps to exactly one output.