Question

Evaluate the function when x = 3. F(x) = -x 2 + 4x – 5A car has a 20 gallon of gas tank. On a long highway trip, gas is used at a rate of about 4 gallons per hour. The gallons of gas g in the car’s tank can be modeled by the equation g= 20- 4t where t is the time in hours. A. Identify the domain and range of the equation. Then graph the equation.

Answer 1

1. The domain of the equation
`g = 20 - 4t is \( t \geq 0 \)`since time cannot be negative.

2. The range of the equation is
`\( g \leq 20 \)`because the gallons of gas cannot exceed the tank's capacity of 20 gallons.

Step-by-step explanation:

For the equation
`\( g = 20 - 4t \),` the domain represents the permissible values of the independent variable, time
`\( t \)`, which in this case is
`\( t \geq 0 \).` This constraint arises because time cannot be negative in the context of this scenario. The range, on the other hand, denotes the possible values of the dependent variable, gallons of gas
`\( g \). Here, \( g \leq 20 \)` because the car's gas tank capacity is 20 gallons, so the amount of gas cannot exceed this limit. Graphically, this equation would yield a straight line with a negative slope, starting at 20 on the y-axis and decreasing steadily as time increases on the x-axis until it reaches zero when the tank is empty.

Understanding the domain and range is crucial in grasping the permissible values and limitations of the variables involved in the equation, ensuring that the model remains practical and aligned with real-world constraints.