Question
The function below shows the cost for mrs franklin to go to a resteraunt with c of her grandchildren. h(c)=6.85+2.95c
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
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 \( h(c) = 6.85 + 2.95c \) which describes the cost for Mrs. Franklin to go to a restaurant with \( c \) of her grandchildren.
1. **Independent variable**: The independent variable is \( c \), which represents the number of grandchildren that Mrs. Franklin takes to the restaurant. It is independent because the cost depends on how many grandchildren she takes.
2. **Dependent variable**: The dependent variable is \( h(c) \), which represents the total cost of her dining out with her grandchildren. It is dependent on the number of grandchildren she brings.
3. **Slope and its meaning**: The slope of the function is \( 2.95 \). This means that for each additional grandchild \( c \) that Mrs. Franklin brings to the restaurant, the cost \( h(c) \) increases by $2.95.
4. **Y-intercept and its meaning**: The y-intercept is \( 6.85 \). This represents the fixed cost (or base cost) for Mrs. Franklin to dine out, even if she brings no grandchildren with her. So, if \( c = 0 \) (no grandchildren), the cost is still $6.85.
5. **Domain**: The domain of the function consists of all non-negative integers (assuming she can only bring whole grandchildren) which is represented as \( c \in \{0, 1, 2, \ldots\} \). In interval notation, this can be expressed as \( [0, \infty) \) for \( c \geq 0 \).
6. **Range**: The range of \( h(c) \) can be determined by plugging in the values from the domain into the cost function. The minimum cost occurs when there are no grandchildren, which is $6.85, and as the number of grandchildren increases, the cost will keep increasing without bound. Thus, the range is \( [6.85, \infty) \).
In summary:
- Independent variable: \( c \) (number of grandchildren)
- Dependent variable: \( h(c) \) (cost)
- Slope: \( 2.95 \) (cost increases by $2.95 for each grandchild)
- Y-intercept: \( 6.85 \) (base cost without any grandchildren)
- Domain: \( [0, \infty) \)
- Range: \( [6.85, \infty) \)
1. **Independent variable**: The independent variable is \( c \), which represents the number of grandchildren that Mrs. Franklin takes to the restaurant. It is independent because the cost depends on how many grandchildren she takes.
2. **Dependent variable**: The dependent variable is \( h(c) \), which represents the total cost of her dining out with her grandchildren. It is dependent on the number of grandchildren she brings.
3. **Slope and its meaning**: The slope of the function is \( 2.95 \). This means that for each additional grandchild \( c \) that Mrs. Franklin brings to the restaurant, the cost \( h(c) \) increases by $2.95.
4. **Y-intercept and its meaning**: The y-intercept is \( 6.85 \). This represents the fixed cost (or base cost) for Mrs. Franklin to dine out, even if she brings no grandchildren with her. So, if \( c = 0 \) (no grandchildren), the cost is still $6.85.
5. **Domain**: The domain of the function consists of all non-negative integers (assuming she can only bring whole grandchildren) which is represented as \( c \in \{0, 1, 2, \ldots\} \). In interval notation, this can be expressed as \( [0, \infty) \) for \( c \geq 0 \).
6. **Range**: The range of \( h(c) \) can be determined by plugging in the values from the domain into the cost function. The minimum cost occurs when there are no grandchildren, which is $6.85, and as the number of grandchildren increases, the cost will keep increasing without bound. Thus, the range is \( [6.85, \infty) \).
In summary:
- Independent variable: \( c \) (number of grandchildren)
- Dependent variable: \( h(c) \) (cost)
- Slope: \( 2.95 \) (cost increases by $2.95 for each grandchild)
- Y-intercept: \( 6.85 \) (base cost without any grandchildren)
- Domain: \( [0, \infty) \)
- Range: \( [6.85, \infty) \)