You can use the definition of domain and range to identity them for the specified plotted function.
The domain and range of the given function is given by
Option B:
- Domain : [tex][0, \infty)[/tex]
- Range : [tex](-\infty, 4][/tex]
What is domain and range of a function?
- Domain is the set of values for which the given function is defined.
- Range is the set of all values which the given function can output.
How are numerical intervals interpreted?
- [a,b] means all values between a and b and including a and b too.
- (a,b] means all values between a and b and including only b.
- For infinity and negative infinity, we cannot write [tex]\infty ][/tex] since we cannot include infinity or negative infinity as they are symbols representing arbitrary large or small numbers respectively.
One more thing to note is that, usually, we plot functions such that inputs are on the horizontal axis(x-axis) and the outputs are on the vertical axis(y-axis).
In the given graph, we can see that the function is not defined for values of x < 0 and thus, we have the domain of the plotted function as [tex]x \geq 0[/tex]
We can write it as [tex]x \in [0, \infty)[/tex]
It can be seen that the function is going down and the maximum value on y-axis it could attain was 4, so the range of the function has maximum value of 4
It can be seen that the function is just going down. Assuming that it goes down and has no lower limit, we can say that the function goes till -infinity.
Thus, its outputs include the values [tex](-\infty, 4][/tex]
Thus,The domain and range of the given function is given by
Option B:
- Domain : [tex][0, \infty)[/tex]
- Range : [tex](-\infty, 4][/tex]
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