1. Let's start by stating the problem: Marcus pays a monthly fee of 20 plus 5 for each premium movie watched, and he wants to spend no more than 50 each month. 2. The cost function can be written as $$y = 20 + 5x$$ where $x$ is the number of premium movies watched and $y$ is the total cost. 3. Since Marcus wants to spend no more than 50, we have the inequality $$20 + 5x \leq 50$$. 4. To find the domain (possible values of $x$), solve the inequality: $$20 + 5x \leq 50$$ $$5x \leq 50 - 20$$ $$5x \leq 30$$ $$x \leq \frac{30}{5}$$ $$x \leq 6$$ 5. Since $x$ represents the number of movies watched, it must be a whole number greater than or equal to 0, so the domain is $$0 \leq x \leq 6$$. 6. To find the range (possible values of $y$), substitute the domain values into the cost function: - When $x=0$, $$y = 20 + 5 \times 0 = 20$$ - When $x=6$, $$y = 20 + 5 \times 6 = 50$$ 7. Therefore, the range is $$20 \leq y \leq 50$$. This means Marcus can watch between 0 and 6 premium movies, and his total cost will be between 20 and 50 inclusive.