Question

4) ** Identify the domain and range of the following functions: X -5 -3 y у 2 1 ان کسر لن 0 - 1 -3 1 Domain Domain: Domain: Range: Range:

Answer 1

By definition, the domain of a function is the set of all values for which the function is defined. And the range is the set of all the values that the function takes.

Then, for the first function, by the arrows on the graph, you can tell that the function continues beyond the grid.

So, the domain of this function is all real numbers.

`D_f=\mathfrak{\Re }`

Looking at the range, you can see that the function takes values from -3, so the range of this function is

`R_f=\lbrack-3,\infty)`

For the second function, you can see that the function is defined for values in x from -5 to -1, then the domain of this function is

`D_f=\lbrack-5,-1\rbrack`

Looking at the range, you can see that the function takes values from -1 to 2, then the range of this function is

`R_f=\lbrack-1,2\rbrack`

Therefore, the domain and range of the functions is

First function

`\begin{gathered} D_f=\mathfrak{\Re } \\ R_f=\lbrack-3,\infty) \end{gathered}`

Second function

`\begin{gathered} D_f=\lbrack-5,-1\rbrack \\ R_f=\lbrack-1,2\rbrack \end{gathered}`