 Hello and welcome to the session. In this session we will discuss how to graph square root and cube root functions. First of all we shall discuss graph of square root functions a function of the type f of x is equal to square root of x is called square root function the domain of this function is set of all positive real numbers and zero because square root of a negative number is not a real number. Now let's discuss graph of square root functions. For this we consider an example. Here we have to graph the function f of x is equal to square root of x minus 2. First of all let us find the domain of the square root function such that expression under the square root must be positive or zero. So x minus 2 should be greater than or equal to zero which implies that x is greater than or equal to 2. So we say that domain is the set of all x greater than or equal to 2 where x belongs to the set of real numbers. Now we make table of values for the given function. We put x values greater than or equal to 2. In this table in the first column we have taken x values which are greater than or equal to 2. So we have taken 2, 3, 6 and 11. Now we shall find the values for f of x for the corresponding values of x. For x is equal to 2 f of x that is f of 2 will be equal to square root of 2 minus 2 that is equal to square root of 0 which is equal to 0. So for x is equal to 2 f of x is equal to 0. Similarly for x is equal to 3 f of x that is f of 3 will be equal to square root of 3 minus 2 that is equal to square root of 1 which is equal to 1. So for x is equal to 3 f of x is equal to 1. Similarly for x is equal to 6 f of x that is f of 6 will be equal to square root of 6 minus 2 that is equal to square root of 4 which is equal to 2. So for x is equal to 6 f of x is equal to 2. Similarly for x is equal to 11 f of x that is f of 11 will be equal to square root of 11 minus 2 that is equal to square root of 9 which is equal to 3. So for x is equal to 11 f of x is equal to 3. Now let us draw its graph. Here we have taken the x values along horizontal axis and the values of f of x along vertical axis. Now this is the graph of the function f of x is equal to square root of x minus 2. From the graph we can see that y takes values greater than or equal to 0. So range of the function will be equal to the semi-closed interval 0 to infinity. This is the required graph of the function f of x is equal to square root of x minus 2 where range is given by the semi-closed interval 0 to infinity and domain is the set of all x greater than or equal to 2 where x belongs to the set of real numbers. Now we shall discuss about graph of cube root functions. Cube root function f is defined by f of x is equal to cube root of x. The domain of this function is set of all real numbers and ranges set of all real numbers. Let us consider an example. We have to grab the function f of x is equal to cube root of x minus 3. Now we know that since it is a cube root function so its domain is set of all real numbers. Let us make its table of values. Now here in this table in the first column we have randomly taken values of x that is minus 5, 2, 3, 4 and 11. Now in the second and third column we shall find the values of x minus 3 and f of x for these corresponding values of x. So for x is equal to minus 5 x minus 3 will be minus 5 minus 3. That is minus 8. For x is equal to 2 x minus 3 is 2 minus 3 that is equal to minus 1. For x is equal to 3 x minus 3 will be 3 minus 3 that is equal to 0. For x is equal to 4 x minus 3 is equal to 4 minus 3 that is 1 and for x x is equal to 11, x minus 3 that is 11 minus 3 will be equal to 8. Now we shall calculate the values of f of x or y. Now for x minus 3 is equal to minus 8, y is equal to cube root of minus 8 which implies that y is equal to minus 2. Similarly for x minus 3 is equal to minus 1, y is equal to cube root of minus 1 which implies that y is equal to minus 1. Similarly we shall find the remaining values of y for the corresponding values of x minus 3 and we have found that for x minus 3 is equal to 0, y is equal to 0, for x minus 3 is equal to 1, y is equal to 1, for x minus 3 is equal to 8 the value of y is 2. So we say that for x is equal to minus 5, y is equal to minus 2, for x is equal to 2, y is equal to minus 1, for x is equal to 3, y is equal to 0, for x is equal to 4, y is equal to 1, and for x is equal to 11, y is equal to 2. Now we shall plot x and y values on the graph. Now we have plotted these values on the graph and then we have joined these points to form this curve and this is the required graph of the function f of x is equal to cube root of x minus 3 and from this graph we can see that range of this function is set of all real numbers. Thus in this session we have discussed how to graph square root and cube root functions. This completes our session. Hope you enjoyed this session.