Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To determine the range of the function [tex]\( m(x) = 30x + 5,000 \)[/tex], let's analyze the function step by step.
1. Understanding the Function:
- The given function [tex]\( m(x) = 30x + 5,000 \)[/tex] represents the total mileage on the car.
- Here, [tex]\( m(x) \)[/tex] is the total mileage and [tex]\( x \)[/tex] is the number of gallons of gas consumed.
2. Interpretation of the Function:
- When [tex]\( x = 0 \)[/tex], the initial mileage of the car is given by [tex]\( m(0) \)[/tex]:
[tex]\[ m(0) = 30 \cdot 0 + 5,000 = 5,000 \][/tex]
So, the car starts with 5,000 miles.
- As [tex]\( x \)[/tex] increases (i.e., more gas is consumed), the mileage [tex]\( m(x) \)[/tex] will also increase because [tex]\( 30x \)[/tex] is a positive term.
3. Identifying the Range:
- Because the function [tex]\( m(x) = 30x + 5,000 \)[/tex] is linear with a positive slope (30), it means that as [tex]\( x \)[/tex] increases from 0 to positive infinity, [tex]\( m(x) \)[/tex] will increase from 5,000 to positive infinity.
- The lowest value of [tex]\( m(x) \)[/tex] occurs at [tex]\( x = 0 \)[/tex], which is 5,000.
Thus, the set of all possible values of [tex]\( m(x) \)[/tex] starts from 5,000 and increases indefinitely. This means that the range of the function can be expressed as:
[tex]\[ [5,000, \infty) \][/tex]
Therefore, the correct answer is:
[tex]\[ [5,000, \infty) \][/tex]
1. Understanding the Function:
- The given function [tex]\( m(x) = 30x + 5,000 \)[/tex] represents the total mileage on the car.
- Here, [tex]\( m(x) \)[/tex] is the total mileage and [tex]\( x \)[/tex] is the number of gallons of gas consumed.
2. Interpretation of the Function:
- When [tex]\( x = 0 \)[/tex], the initial mileage of the car is given by [tex]\( m(0) \)[/tex]:
[tex]\[ m(0) = 30 \cdot 0 + 5,000 = 5,000 \][/tex]
So, the car starts with 5,000 miles.
- As [tex]\( x \)[/tex] increases (i.e., more gas is consumed), the mileage [tex]\( m(x) \)[/tex] will also increase because [tex]\( 30x \)[/tex] is a positive term.
3. Identifying the Range:
- Because the function [tex]\( m(x) = 30x + 5,000 \)[/tex] is linear with a positive slope (30), it means that as [tex]\( x \)[/tex] increases from 0 to positive infinity, [tex]\( m(x) \)[/tex] will increase from 5,000 to positive infinity.
- The lowest value of [tex]\( m(x) \)[/tex] occurs at [tex]\( x = 0 \)[/tex], which is 5,000.
Thus, the set of all possible values of [tex]\( m(x) \)[/tex] starts from 5,000 and increases indefinitely. This means that the range of the function can be expressed as:
[tex]\[ [5,000, \infty) \][/tex]
Therefore, the correct answer is:
[tex]\[ [5,000, \infty) \][/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.