Find the domain and range of the function from the graph.
We can see the graph does not go beyond -1 on the x axis on the left and not beyond 2 on the right
The domain -1 $\leq $ x $\leq $ 2
It can also be written as [-1, 2]
The range we look at the smallest y value, which is 1 and the highest value is 10
The range 1 $\leq $ y $\leq $ 10
In the interval notation it can be written as [1,10]
Find the domain and range from the given graph
Looking left to right, we see the first x value is at -5 and we see even though the graph is broken, the y value exist at the broken part of the curve so x is still defined till x=9 which is denoted by a hollow circle which means x is not included.
The domain is [-5, 9)
Range : we can see that the graph does not cross 3 and the lowest point is y=1.
The range [1, 3]
How can you tell whether a graph is the graph of a function?
First we need to understand the definition of the function which says that for every x there is exactly one y value. To check if the given graph is a function, one just need to apply the vertical line test. If at any x value the line passes through 2 or more point on the curve then the given graphs is not the graph of a function.
Is the given graph a function?
NO, when we draw a vertical line it intersects at more than one point.
Is the graph a graph of a function
When we draw the vertical line it intersects at only one point