 Hello and welcome to the session. In this session we will discuss the graphs of exponential and logarithmic functions showing Intercepts and End Behavior. Also we will discuss graphs of trigonometric functions showing periods, width line and amplitude. First of all let us discuss the graphs of exponential and logarithmic functions showing intercepts and end behavior. Now we know that the equation f of x is equal to b raised to power x where b is greater than 0 and b is not equal to 1 defines an exponential function for each different constant b of the base. The independent variable x may assume any real value. The functional value will be positive because a positive base raised to any power is positive. This means that graph of the exponential function f of x is equal to b raised to power x will be located in the first and second quadrant because in these two quadrants for any value of x, y is positive and logarithmic functions are the inverse of exponential functions. Now for x is greater than 0, a is greater than 0 and a is not equal to 1. We have y is equal to log x to the base a if and only if x is equal to a raised to power y since x is greater than 0, so the graph of this logarithmic function will be in first and fourth quadrant as in these two quadrants for any value of y, x is always positive. Now let us discuss an example. Here we will draw graphs of the given functions. First is y is equal to 3 raised to power x and second is y is equal to log x to the base 3. First of all let us draw the graph of this exponential function. For this we will make table of values. First of all let us put x is equal to minus 3 in this equation. So for x is equal to minus 3 we get y is equal to 3 raised to power minus 3 which is equal to 0.04. Then for x is equal to minus 2 we get y is equal to 0.1. For x is equal to minus 1 we have y is equal to 0.3. Similarly we have obtained all these values of x and y. Now let us plot all these points on the graph. So we have plotted all these points on the graph. Now drawing out all these points we get the graph of the exponential function y is equal to 3 raised to power x. Now here we can see this curve cuts the y axis at the point 0,1. So its y-intercept is equal to 1 and this curve will never cut the x axis so the function has no x-intercept. Also here you can see as x tends to infinity y tends to infinity and here you can see as x tends to minus infinity y tends to 0. Now let us discuss the graph of logarithmic function y is equal to log x to the base 3. By definition we know that y is equal to log x to the base 3 if and only if x is equal to 3 raised to power y. Now let us make the table of values. Now here let us put y is equal to minus 2 in this equation. So putting y is equal to minus 2 we get x is equal to 3 raised to power minus 2 which is equal to 0.1. Similarly we obtain all these values of x and y. Now we will plot all these points on the graph. Now here we have plotted all these points on the graph and joining all these points we get the graph of logarithmic function y is equal to log x to the base 3. Now here you can see this curve cuts the x-axis at this point that is the point which coordinates 1, 0. So its x-intercept is equal to 1 and this curve will never cut the y-axis so the function has no y-intercept. Also we see that as x tends to infinity y tends to infinity and here you can see as x tends to 0 y tends to minus infinity. So this is the graph of this logarithmic function. Now let us discuss graph of trigonometric functions showing period, amplitude and midline. Now let us see this graph of a trigonometric function. Here we have to find period, amplitude and midline of this function. Now period is length of one cycle and for this curve length of one cycle is pi minus pi by 3. Now this is equal to 3 pi minus pi whole upon 3 which is equal to 2 pi by 3. So period of this trigonometric function is 2 pi by 3. Now let us find the midline. Now midline of a periodic function is the horizontal line midway between the functions maximum and minimum values. So midline is equal to maximum value plus minimum value whole upon 2. For this function this point is maximum and this point is minimum. Now maximum point is at y is equal to 2 and minimum point is at y is equal to minus 4. So midline is equal to 2 plus of minus 4 whole upon 2 which is equal to minus 2 upon 2 that is equal to minus 1. So equation of midline is y is equal to minus 1. So here this pink line is the midline of this function and its equation is y is equal to minus 1. Now we have to find amplitude. Now amplitude is the vertical distance between functions maximum or minimum value and the midline. So here let us find this distance between the functions maximum value and the midline. So amplitude is equal to maximum value that is 2 minus midline that is y is equal to minus 1 which is equal to 2 plus 1 that is equal to 3. So amplitude is equal to 3. So we have determined period midline and amplitude of this trigonometric function. So in this session we have discussed graphs of exponential and logarithmic functions showing the intercepts and nth behavior. Also we have discussed trigonometric functions showing period midline and amplitude. This completes our session. Hope you all have enjoyed the session.