Question

representing a situation with a linear function
a video game arcade offers a yearly membership with reduced rates for game play. a single membership costs $60 per year. game tokens can be purchased by members at the reduced rate of $1.00 per 10 tokens.
which statements represent the function of the yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? select three answers.

• the slope of the function is $1.00.
• the y - intercept of the function is $60
• the function can be represented by the equation $y = \frac{1}{10}x + 60$
• the domain is all real numbers
• the range is ${y|y \geq 60}$

Explanation:

Step1: Define cost components

The fixed cost (membership) is $60, and the variable cost is $\frac{\$1.00}{10 \text{ tokens}} = \$0.10$ per token.

Step2: Form linear function

Let $x$ = number of tokens, $y$ = total cost. The function is $y = \frac{1}{10}x + 60$.

Step3: Analyze slope/intercept

Slope = variable cost per token = $\frac{1}{10} = 0.10$, y-intercept = fixed membership cost = 60.

Step4: Analyze domain/range

Domain: $x$ is non-negative integers (can't buy negative tokens), not all real numbers. Range: $y \geq 60$ (minimum cost is the membership fee, increases with tokens).

Answer:

• The y-intercept of the function is $60.
• The function can be represented by the equation $y = \frac{1}{10}x + 60$.
• The range is $\{y| y \geq 60\}$