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“Is equal to square root of x. This is a function in x. Before we we look at its graph can you guess the domain of this function domain is set of values x. Can take the domain will be all x.
Greater than or equal to zero. As even roots cannot have negative numbers under them. Now let s draw its graph. As the domain is greater than or equal to zero.
We just try out non negative values of x when x is zero root of x will also be 0 0 comma 0. Will be our first point what is y when x is 1 root of 1 is also 1. So 1 comma. 1.
Is another point. When x. Is 2. Y.
Will be square root of 2. Which equals. 1 point. 4 1.
4. Somewhere. Here this is how the graph will look. It is not a straight line as the function is not linear.
Interesting what if i negate this function. Now. What will the graph of minus root x. Look like the first thing.
We should do before plotting a graph is examine the domain as x lies under the square root. It has to be non negative the domain again will be all x greater than or equal to 0 try substituting different non negative values of x and plot this functions graph ok. I m sure most of you guys would have got the correct graph. When x is 0.
Y will also be 0. This will be one of the points. When x. Is 1 y.
Will be minus 1 1. Comma. Minus. 1.
Will be another point. And. When. X is 2.
Y will equal minus 1. Point. 4 1. 4.
This is an approximate graph of the function y is equal to minus root x. What do you notice this graph is a reflection of the graph of the original function. And it is a reflection about the x axis negating. The function reflects it about the x axis okay good.
But what if we negate just the input. Say. The function is y. Is equal to root of minus x.
Find the domain. First and then try plotting its graph. The domain is interesting here. The value under an even root cannot be negative.
So minus x. Cannot be negative. 4 minus x to be non negative x has to be a non positive that s because the negative of a negative number will be positive. So the domain here will be all x less than or equal to 0.
Now let s plot the graph by substituting a few non positive numbers in place of x. When. X. Is 0.
Y. As well is 0. When x is. Minus 1.
Y. Will be root of minus of minus. 1. That will be 1.
When. X. Is minus 2. Y.
Will be one point. 4 1. 4. This will be the graph of the third function compare it to the original one its reflected about the y axis.
All this is so easy. But can get complicated if you don t understand how graphs are drawn let s summarize. What we saw in this session. If y is equal to f of x.
Is the original function then the graph of y equal to minus f of x. Will reflect about the x axis. And the graph of y equal to f. Of minus x.
Will reflect about the y axis. Don t worry in the next session. We will review what we did in this session and in the previous one as well ” ..
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