Given:
The graph of a function.
To find:
The domain and range of the given function.
Solution:
Domain: It is the set of input values.
Range: It is the set of output values.
From the given graph, it is clear that the function is defined for all real values of x because it is a downwards parabola. So, domain is the function is the set of all real number.
[tex]Domain=\{x|x\in R\}[/tex]
[tex]Domain=(-\infty,\infty)[/tex]
The function is maximum at point (0,7). So, the maximum value of the function is 7. So, the range of the function is the set of all real numbers less than or equal to 7.
[tex]Range=-\infty<y\leq 7[/tex]
[tex]Range=(-\infty,7][/tex]
Therefore, the domain of the function is [tex](-\infty,\infty)[/tex] and the range of the function is [tex](-\infty,7][/tex].