We have to find the domain before we can find the range.
Domain: 0≤ b ≤ 8 Range: 0≤ A(b) ≤ 9600 Explanation: See solution.
Practice makes perfect
Finding the Domain
Let's recall what domain represents. The domain is the set of the possible inputs into a function.
A(b) = 1200b
In our function b is the variable for inputs, which represents bags of grass seed. We will try to find the set of values for b that makes sense for the given scenario. Since we are told that we only have 8 bags of grass seed, the largest value possible for b is 8.
A(b) = 1200b where b≤8
Furthermore, it would not make sense to use a negative amount of bags of grass seed, so b also must be greater than or equal to zero.
A(b) = 1200b where 0 ≤ b≤8
Therefore our domain is 0 ≤ b ≤ 8, because we can use between 0 and 8 bags of grass seed.
Finding the Range
Now, let's recall the range of a function. The range represents the set of all of the possible outputs of a function.
A(b) = 1200b where 0 ≤ b≤8
In our function A(b) is the output variable, so we will try to find the set of values for A(b). Let's substitute the smallest possible input, 0, into our function to find the smallest possible output.
A(0)=1200(0) ⇒ A(0)=0
Now let's substitute the largest possible input, 8, into our function to find the largest possible output.
A(8)=1200(8) ⇒ A(8)=9600
Thus, we have found that the smallest output is 0 and the largest output is 9600. This means that the range is 0≤ A(b) ≤ 9600.
