Let's analyze the function \( f(r) = 1.75 + 5 \).
1. Independent and Dependent Variables
- Independent Variable: The independent variable is \( r \), which represents the number of rides taken at the fair.
- Dependent Variable: The dependent variable is \( f(r) \), which represents the total cost to attend the fair based on the number of rides taken.
2. Slope and its Meaning
In the given function \( f(r) = 1.75 + 5 \), it seems that the expression should probably reflect a more complex relationship where the variable \( r \) is multiplier or coefficient, but as given, is constant. Interpreting this, the slope in traditional slope-intercept form \( y = mx + b \) does not directly apply in this form.
Since the function does not explicitly show \( r \) as a factor affecting the cost, the slope would effectively be:
- Slope: There is no slope in the traditional sense as \( r \) does not appear as a variable multiplied to any coefficient.
3. Y-Intercept and its Meaning
- Y-Intercept: The expression simplifies to \( f(r) = 6.75 \). So if we examine it more closely, the function does not contain \( r \) in the form we might expect, leading to:
- The implied cost (y-intercept) when no rides are taken could simply be a fixed cost of \( 6.75 \) (based on understanding).
4. Domain
- Domain: Since \( r \) represents the number of rides taken, the domain is typically all non-negative integers (whole numbers representing rides taken). Therefore, the domain is: \[ \text{Domain: } r \geq 0 \quad (r \in \mathbb{Z}^+) \]
5. Range
- Range: Considering \( f(r) = 6.75 \) irrespective of \( r \), the cost remains constant. Thus, the range is the single value: \[ \text{Range: } { 6.75 } \]
Summary:
- Independent Variable: \( r \) (the number of rides)
- Dependent Variable: \( f(r) \) (the total cost)
- Slope: Not applicable (or considered to be 0 in this case)
- Y-Intercept: 6.75 (represents a fixed cost)
- Domain: \( r \geq 0 \) (non-negative integers)
- Range: \( { 6.75 } \) (fixed cost)
If the function is meant to involve more interactions between the number of rides and costs, please clarify to provide a function that might actually show an increasing cost per ride.
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