Let's analyze the function given:
\[ f(t) = 1.90 + 1.40t \]
Independent and Dependent Variables:
- Independent Variable: The independent variable is \( t \), which represents the number of toppings on the hamburger. It is the variable that you can control or change.
- Dependent Variable: The dependent variable is \( f(t) \), which represents the cost of the hamburger based on the number of toppings. It depends on the number of toppings chosen.
Slope and Its Meaning:
- Slope: The slope of the function is \( 1.40 \). This indicates that for every additional topping added to the hamburger, the cost increases by $1.40.
Y-Intercept and Its Meaning:
- Y-Intercept: The y-intercept of the function is \( 1.90 \). This means that when there are no toppings (\( t = 0 \)), the base cost of the hamburger is $1.90.
Domain:
The domain of the function is the set of all possible values for \( t \). Since you cannot have a negative number of toppings, the domain is:
\[ \text{Domain: } t \geq 0 \]
In interval notation, this is expressed as:
\[ [0, \infty) \]
Range:
The range of the function consists of all possible values of \( f(t) \). As \( t \) increases from 0 to infinity, the cost \( f(t) \) increases without bound. The minimum value of \( f(t) \) occurs when \( t = 0 \):
\[ f(0) = 1.90 \]
So the range of the function is:
\[ \text{Range: } f(t) \geq 1.90 \]
In interval notation, this is expressed as:
\[ [1.90, \infty) \]
Summary:
- Independent variable: \( t \) (number of toppings)
- Dependent variable: \( f(t) \) (cost of the hamburger)
- Slope: \( 1.40 \) (cost per additional topping)
- Y-intercept: \( 1.90 \) (base cost of the hamburger)
- Domain: \( [0, \infty) \)
- Range: \( [1.90, \infty) \)