Question
THe function below shows the cost to attend the fair if you ride(r) rides
f(r)=1.75+5
what is the independent variable
what is the dependent variable
what is the slope and its meaning
what is the y-intercept and its meaning
find domain
find range
f(r)=1.75+5
what is the independent variable
what is the dependent variable
what is the slope and its meaning
what is the y-intercept and its meaning
find domain
find range
Answers
GPT-4o mini
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.
### 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.