00:01
In part a, we find the domain and range of the function using the graph of this function.
00:07
So domain is basically the all input values or the all possible values of x, where the graph of the function is defined.
00:16
So when we see the graph from the left to right, we see that the graph of the function is defined for all x values on the number line.
00:24
So therefore, we say that the domain of the function is all real numbers.
00:29
Or in interval notation we can say that the domain of this function is from negative infinity to positive infinity and so this is the domain of the function now let's determine the range of this function the range of the function is the all possible values of y where the graph of the function is defined and when we see the graph of the function we see that the graph starts at negative 4 that is the lowest value of the y is negative 4 and the greatest value it extends to infinity.
01:06
So we see that the range of this function is from negative 4 to infinity.
01:20
You know answer part b.
01:23
Here we have to determine the zeros of f.
01:26
Zero's of the function f is the points where the graph of the function becomes zero.
01:33
Or graphically we can see that wherever the graph intersects the x -axis, so we have to consider those points as the zeros of the f.
01:42
Also, wherever it touches the graph of the, it touches the x -axis, we see that it is also the zero of the function f.
01:51
So from this graph of the function, we say that at x equal to negative 3, we see that the graph is intersecting the x -axis, and at x equal to 2, we see that the graph touches the x -axis and at x -equal to 5.
02:07
We see that the graph is intersecting the x -axis.
02:10
So basically we have three zeros of this function.
02:14
So therefore we see that the zeros of this function is negative 3, 2 and 5.
02:25
Let's answer part c.
02:27
Here we have to determine the open intervals in which the graph is increasing, decreasing and constant.
02:35
So first let's determine the open intervals in which the function is increasing.
02:39
We say that the function is increasing as x increases the graph of the function should increase that is the y should also increase so when we see the graph from left to right we see that at this point that is when x equal to this is approximately negative 1 .5 from this point to till this is increasing increasing and here it becomes so zero so till x equal to 2 it is increasing this this is one open interval.
03:11
So i mentioned that that is from negative 1 .5 to 2.
03:15
This is increasing.
03:17
Let's find if there are any other intervals.
03:20
We also see that approximately when x equal to this is, let's see this is 4 .2.
03:26
From this point to when x approaches this is infinity, it keeps on increasing.
03:33
So we see that there is another open interval.
03:36
So we put union and then from 4 .2.
03:39
To infinity the graph is increasing.
03:43
So this is the interval in which the graph of the function is increasing.
03:50
Now let's find the interval where the function is decreasing.
03:55
So when x increases, y should decrease.
03:58
So that is the interval we see that the function is decreasing.
04:03
So when you see the graph from left to right, when x comes from negative infinity to positive infinity we see that the function is decreasing till it reaches the point that is exactly this point which is negative 1 .5 so one of the interval where it is decreasing is from negative infinity to negative 1 .5 we say that the function is decreasing let's find out if there are any other intervals where it is decreasing if we observe that when x equal to 2 from this point it is decreasing till it reaches exactly 4 .2...