Question

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

Fixed cost (membership): $\$60$. Variable cost per token: $\frac{\$1}{10} = \$0.10$.

Step2: Formulate cost function

Total cost $y$ = variable cost + fixed cost:
$$y = \frac{1}{10}x + 60$$

Step3: Analyze slope

Slope = variable cost per token = $\frac{1}{10} = 0.10$, not $\$1.00$.

Step4: Analyze y-intercept

y-intercept = fixed cost = $\$60$ (cost when $x=0$).

Step5: Analyze domain

$x$ = number of tokens, so $x$ is non-negative integers (not all real numbers).

Step6: Analyze range

Minimum cost is $\$60$ (when $x=0$), cost increases with $x$, so range is $\{y \mid y \geq 60\}$.

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 $\{y\mid y \geq 60\}$.