To address this question, we need to analyze the relationship between the yearly cost in dollars, [tex]\( y \)[/tex], and the number of game tokens purchased, [tex]\( x \)[/tex]. Let's break this down step-by-step.
1. Cost Analysis:
- The yearly membership cost is a fixed value of [tex]$60.
- The tokens are purchased at the rate of \$[/tex]1.00 for every 10 tokens. This means the rate for each token is [tex]\(\frac{1}{10}\)[/tex] dollars.
2. Constructing the Function:
- The total cost [tex]\( y \)[/tex] is the sum of the yearly membership fee and the cost of the tokens. This can be modeled by the equation [tex]\( y = \frac{1}{10} x + 60 \)[/tex], where [tex]\( x \)[/tex] is the number of tokens purchased.
3. Identifying the Slope:
- The slope of the function indicates the cost per token, which is [tex]\(\frac{1}{10}\)[/tex] dollars.
4. Identifying the y-intercept:
- The y-intercept of the function is the cost when no tokens are purchased. This is the membership fee of \[tex]$60.
5. Domain and Range:
- Domain: The domain of the function essentially refers to all possible values of \( x \). Since it's possible to purchase any number of tokens (assuming we can have non-integer values for this scenario), the domain is all real numbers.
- Range: The range of the function refers to all possible values of \( y \). Since the minimum cost is the membership fee (i.e., y ≥ 60), the range is \(\{ y \mid y \geq 60 \}\).
Now we can select the correct applicable statements:
1. The slope of the function is \(\frac{1}{10}\), not \$[/tex]1.00.
2. The [tex]\( y \)[/tex]-intercept of the function is \[tex]$60.
3. The function can be represented by the equation \( y = \frac{1}{10} x + 60 \).
4. The domain is all real numbers.
5. The range is \(\{ y \mid y \geq 60 \}\).
So, the three correct statements are:
- The \( y \)-intercept of the function is \$[/tex]60.
- The function can be represented by the equation [tex]\( y = \frac{1}{10} x + 60 \)[/tex].
- The domain is all real numbers.
- The range is [tex]\(\{ y \mid y \geq 60 \}\)[/tex].
