00:03
We are given the graph of a function and we're asked to find the domain and range of this function and we are given function values and we're asked to find these function values.
00:15
So our function is depicted in the graph following exercise 8 of this section.
00:22
To determine the domain of this function, well, we look at our graph and we want to see how far the function extends in either direction from left to right.
00:40
So, even though it appears that the function is not defined for x greater than or equal to 2, one could make the argument that we just ran out of space to draw the rest of the graph.
01:02
In fact, the domain here, we see that for every x value, there is an associated y value on the graph, even if it's not pictured here.
01:18
So, the domain of our function, f, an interval notation, this is the interval negative infinity to positive infinity, or the set of all real numbers are.
01:39
Likewise to find the range, we want to look at the y -axis.
01:47
So given a point on the y -axis, is there a point on the x -axis for which the two coordinates together lie on our graph? so looking up and down the y -axis, if we draw horizontal lines to the graph, do we intersect the graph everywhere? it does appear that no matter where you start on the y -axis, if you draw a horizontal line, you will intersect the graph at some point.
02:29
And therefore, it follows up the range of our function, f, is also the interval negative infinity to infinity, or the set of all real numbers are...