When a function is plotted, the domain and the range of the function are the x-coordinate and the y-coordinate respectively. The domain and range of the assumed function for Melissa's garden are: [tex]x = (2,\infty][/tex] and [tex]p(x) = (0,\infty][/tex], respectively.
The function for Melissa's garden is not given. So, I will give a general explanation to calculate domain and range.
The domain is all possible values the independent variables of a function can take while the range is all possible values the dependent variables of a function can take
Assume the function of Melissa's garden is:
[tex]p(x) = x(x - 2)[/tex]
Start by equating the function to 0
[tex]x(x - 2) = 0[/tex]
Split
[tex]x = 0\ or\ x - 2 = 0[/tex]
Solve
[tex]x = 0\ or\ x = 2[/tex]
The above values of x will give [tex]p(x) = 0[/tex]
Because it is a garden, the length of the garden cannot be 0 or less.
So, the domain of the function is:
[tex]x = (2,\infty][/tex]
This means that the domain starts from a value greater than 2 (e.g. 3) and ends at infinity
To calculate the range, we substitute [tex]x = (2,\infty][/tex] in the function
[tex]x = 2[/tex] means
[tex]p(2) = 2 \times ( 2- 2) = 0[/tex]
[tex]x = \infty[/tex] means
[tex]p(2) = \infty \times (\infty- 2) = \infty[/tex]
So, the range of the function is:
[tex]p(x) = (0,\infty][/tex]
This means that the domain starts from a value greater than 0 (e.g. 1) and ends at infinity
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