Question
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 yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Select the three that apply.
(3 points)
Responses
The y-intercept of the function is $60.
The y-intercept of the function is $60.
The domain of the function is all real numbers.
The domain of the function is all real numbers.
The range of the function is y≥60
.
The range of the function is y is greater than or equal to 60.
The function can be represented by the equation y=110x+60
The function can be represented by the equation y is equal to 1 tenth x plus 60
The slope of the function is $1
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 yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Select the three that apply.
(3 points)
Responses
The y-intercept of the function is $60.
The y-intercept of the function is $60.
The domain of the function is all real numbers.
The domain of the function is all real numbers.
The range of the function is y≥60
.
The range of the function is y is greater than or equal to 60.
The function can be represented by the equation y=110x+60
The function can be represented by the equation y is equal to 1 tenth x plus 60
The slope of the function is $1
Answers
GPT-4o mini
To determine the correct statements representing the function of yearly cost in dollars \( y \) based on \( x \), the number of game tokens purchased for a member of the arcade, let's analyze the situation:
1. **Membership Cost**: The membership costs $60 per year.
2. **Cost of Tokens**: Members can buy tokens at the rate of $1.00 for 10 tokens, which means the cost per token is $0.10.
Based on this information, the total yearly cost \( y \) can be modeled by the equation:
\[ y = 60 + 0.10x \]
where \( x \) is the number of tokens purchased.
Now let's examine the statements one by one:
1. **The y-intercept of the function is $60.**
- This is correct because when \( x = 0 \) (no tokens purchased), \( y = 60 + 0.10(0) = 60 \).
2. **The domain of the function is all real numbers.**
- This is incorrect. The number of tokens purchased (\( x \)) cannot be negative, so the domain would be \( x \geq 0 \).
3. **The range of the function is \( y \geq 60 \).**
- This is correct. The minimum yearly cost is $60, and it increases as more tokens are purchased. Therefore, the range is \( y \geq 60 \).
4. **The function can be represented by the equation \( y = 110x + 60 \).**
- This is incorrect. The function has a slope of \( 0.10 \), not \( 110 \).
5. **The slope of the function is $1.**
- This is incorrect. The slope is \( 0.10 \) (the cost per token).
Based on this analysis, the correct three statements are:
1. The y-intercept of the function is $60.
2. The range of the function is \( y \geq 60 \).
3. The function can be represented by the equation \( y = 60 + 0.10x \) (though this exact wording was not an option).
Unfortunately, none of the exact representations of the remaining correct options are stated cleanly; however, it is clear the slope is \( 0.10 \) and the membership fee is \( 60 \).
So the selected statements should be based on the provided points of validity:
1. The y-intercept of the function is $60.
2. The range of the function is \( y \geq 60 \).
3. The slope of the function correctly would be denoted as \( 0.10 \); therefore, the essence lies in identifying correct interpretations only.
Due to limitations presented in exact phrasing, ensure the context adheres to proper guidelines as outlined.
1. **Membership Cost**: The membership costs $60 per year.
2. **Cost of Tokens**: Members can buy tokens at the rate of $1.00 for 10 tokens, which means the cost per token is $0.10.
Based on this information, the total yearly cost \( y \) can be modeled by the equation:
\[ y = 60 + 0.10x \]
where \( x \) is the number of tokens purchased.
Now let's examine the statements one by one:
1. **The y-intercept of the function is $60.**
- This is correct because when \( x = 0 \) (no tokens purchased), \( y = 60 + 0.10(0) = 60 \).
2. **The domain of the function is all real numbers.**
- This is incorrect. The number of tokens purchased (\( x \)) cannot be negative, so the domain would be \( x \geq 0 \).
3. **The range of the function is \( y \geq 60 \).**
- This is correct. The minimum yearly cost is $60, and it increases as more tokens are purchased. Therefore, the range is \( y \geq 60 \).
4. **The function can be represented by the equation \( y = 110x + 60 \).**
- This is incorrect. The function has a slope of \( 0.10 \), not \( 110 \).
5. **The slope of the function is $1.**
- This is incorrect. The slope is \( 0.10 \) (the cost per token).
Based on this analysis, the correct three statements are:
1. The y-intercept of the function is $60.
2. The range of the function is \( y \geq 60 \).
3. The function can be represented by the equation \( y = 60 + 0.10x \) (though this exact wording was not an option).
Unfortunately, none of the exact representations of the remaining correct options are stated cleanly; however, it is clear the slope is \( 0.10 \) and the membership fee is \( 60 \).
So the selected statements should be based on the provided points of validity:
1. The y-intercept of the function is $60.
2. The range of the function is \( y \geq 60 \).
3. The slope of the function correctly would be denoted as \( 0.10 \); therefore, the essence lies in identifying correct interpretations only.
Due to limitations presented in exact phrasing, ensure the context adheres to proper guidelines as outlined.