SL 2.4—Features of a graph

The candle starts at $t=0$ and stops burning when it reaches zero length. We need to find when $L(t)=0$.

Set $L(t)=0$: $20-2.5t=0⟹t=\frac{20}{2.5}=8$ So the candle is fully burned after 8 hours.

Since $t$ represents time, it cannot be negative, and the model is only valid until the candle is gone. The domain is $0\le t\le 8$.

The domain in context is $0\le t\le 8$, which corresponds to the first option.

We need the domain — the valid set of input values ($t$) — constrained by the physical context of the candle burning.

At $t=20$, $L(20)=20-50=-30$ cm, which is physically impossible. The candle cannot have negative length, so this interval is too large.

This ignores the upper boundary. The candle only exists for a finite time — allowing $t$ to grow without bound is not physically meaningful.

This describes the range (output values $L$), not the domain (input values $t$). The question specifically asks for the domain.

The candle burns from $t=0$ to $t=8$ (when $L=0$), so the correct domain is $0\le t\le 8$.

The range is the set of all possible output values ($L$-values) produced by the function over its valid domain.

At $t=0$: $L(0)=20$ cm (full candle). At $t=8$: $L(8)=20-20=0$ cm (fully burned). Since $L(t)$ is linear and decreasing, all values between 0 and 20 are achieved.

The candle length varies from 20 cm down to 0 cm, so the range is $0\le L\le 20$.

The range of $L(t)$ in context is $0\le L\le 20$.

We need the range — the valid set of output values $L$ — given the physical context of a burning candle.

This is the domain (input values $t$), not the range (output values $L$). It does not answer the question.

This correctly excludes negative lengths but ignores the upper bound. The candle cannot be longer than 20 cm (its starting length), so $L\le 20$ must also be included.

This allows negative lengths, which is physically impossible for a candle. The range cannot extend below zero.

Only $0\le L\le 20$ correctly captures all physically valid output values of the candle-length function.