Question

Jim and his dad want to find the length of the garden once they decide its width. Use function notation to write a function that represents its length in terms of the width.

A. l(w)=35−2w
B. l(w)=17.5−w
C. l(w)=35−w
D. l(w)=0.5(35−w)

If the width of the flower bed is 15 feet, what is its length? Write your answer as an evaluation of a function.
A. l(15)=5
B. l(15)=25
C. l(15)=10
D. l(15)=20

If Jim and his dad decide to decrease the width of the flower bed from 15 feet, what happens to its length?
A. Increases
B. Decreases
C. Stays the same
D. Doubles

What is the domain of the function f(w)=0.5(35–2w)? Explain your answer.
A. w≤17.5
B. w≥17.5
C. w>17.5
D. w<17.5

Answer 1

Without specific details on the dimensions of the garden, selecting the correct function from the options provided is not possible. If you have a function like l(w)=35-2w, then the length when the width is 15 feet would be l(15)=5. The domain of f(w)=0.5(35-2w) would be all widths w less than or equal to 17.5 feet since we consider only positive lengths.

Step-by-step explanation:

To write a function that represents the length of the garden in terms of its width, we need to understand the relationship between those two dimensions. Without specific details about the garden's area or other dimensions, it is impossible to determine the correct function from the options provided.

However, assuming you have a specific relationship in mind, based on the function options given, you can evaluate the length when the width is known. If the width is set to 15 feet, you input this value into the chosen function to find the corresponding length. For example, using option A l(w)=35-2w, if w=15, then l(15)=35-2(15)=35-30=5.

If the width of the garden decreases, normally, according to functions like option A, the length would increase as suggested by the negative coefficient in front of w. This assumes a linear relationship where the total area might be constant, and reducing the width necessitates an increase in length to maintain the same area.

Concerning the domain of the function f(w)=0.5(35-2w), it depends on the physical constraints of the garden. If we consider only positive lengths, the width at which the length becomes zero is the upper limit of the domain. Solving for w when the length is zero:
0=0.5(35-2w)
0=35-2w
2w=35
w=17.5
So, the domain would be all widths w that are less than or equal to 17.5 feet, hence the domain is w≤17.5.