You are packing books into a box. The box can hold at most 10 books. The function y=5.2x represents the weight y (in pounds) of x books.
a. Is 52 in the range? Explain.
b. Is 15 in the domain? Explain.
C. Is the domain discrete or continuous?
Book and represent
a. To determine if 52 is in the range of the function y = 5.2x, we need to check if there exists a valid input value of x that results in y = 52. Rearranging the equation, we have x = y / 5.2.
So, if we substitute y = 52 into the equation, we get x = 52 / 5.2 = 10.
Therefore, 52 is in the range of the function y = 5.2x, as it corresponds to a valid value of x (10 books).
b. To determine if 15 is in the domain of the function y = 5.2x, we need to check if there exists a valid output value of y that satisfies the equation for some input value x.
Rearranging the equation, we have x = y / 5.2.
So, if we substitute x = 15 into the equation, we get y = 15 / 5.2 = 2.8846 (rounded to four decimal places).
Therefore, 15 is in the domain of the function y = 5.2x, as it corresponds to a valid value of y (2.8846 pounds, rounded).
c. The domain of the function y = 5.2x represents the possible input values, which is the number of books in this case. Since the number of books can take on any non-negative integer value (0, 1, 2, 3, ...), the domain is discrete.
a. To determine if 52 is in the range of the function y = 5.2x, we need to substitute the value of x into the function and check if it produces the value of 52 for y.
Let's solve the equation 5.2x = 52 for x:
5.2x = 52
Dividing both sides of the equation by 5.2, we get:
x = 10
So, when x = 10 books, the weight y is 52 pounds. Therefore, 52 is in the range of the function.
b. To determine if 15 is in the domain of the function y = 5.2x, we need to understand what the domain represents. In this case, x represents the number of books. Since books are discrete quantities (whole numbers that cannot be in between), we need to check if 15 is a valid number of books to pack into a box.
Since the box can hold at most 10 books (according to the problem statement), it means that x, the number of books, cannot be greater than 10. Therefore, 15 is not in the domain of the function because it exceeds the maximum value allowed for x.
c. The domain of the function y = 5.2x represents the valid values that x (the number of books) can take. In this case, since the box can hold at most 10 books, the domain is the set of integers from 0 to 10 inclusive. This makes the domain discrete because it consists of distinct, separate values with no continuity in between.
a. the range of x is zero to 10
b. if 15=5.2x, x=2.8 which is not allowed, x is discrete
c. domain is discrete. 0,5.2, 10.4, ...