Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
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 appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.