When looking at this problem, we want F of X equaling 4, cosine X. So we're graphing in this instance. So remember, our amplitude is going to be the absolute value of the number in front of the trig function, or our sine or cosine which is 4. Our period is going to be the regular. In this case 2π divided by the number that's multiplied by the X, in this case one. There is no phase shift because we don't have any parenthesis to set equal to 0, so we could think about just letting X = 0. And there is no vertical translation because there was no plus or minus a number with the trig function. So from this we should be able to graph and then answer our questions. Remember, cosine graph usually starts at 01, but because the amplitude is 4, it's going to now start at 04 and then it's going to come down and through and it keeps going for forever. So even though we're going to put some key points here, we're going to know that it keeps going. So when it asks us what is the Y intercept of the graph, what AY intercept means is when X is 0 what is Y? So if we have F of 0X is 04 times cosine zero. Well cosine of 0 is 1 so 4 * 1 would give us 4. So our Y intercept would be 4. So if I go back to my problem, we have AY intercept of four. The next part says for what numbers X negative π less than or equal to X less than or equal to π is the graph of F decreasing? Well, if we go back to our graph, decreasing from negative π to π decreasing means going down South from negative π to 0. It's increasing, it's going up. So from zero to π it's going down. So if we go back to our problem from zero to π remember, symbols are over there. Check our answer. Sorry, I don't have all of these worked out already. What's the absolute maximum of F? Well, what's the highest that that graph ever went? And the highest it ever went was 4. And then for what numbers X from -2π to 2π does F of X equal 4? So we want to know all the maximum points. So if we come back to our graph in between -2π and 2π. So remember here is going to be our -2π. So we have a maximum at -2π, a maximum at zero, and a maximum at 2π. So says use, to separate the answers, type exact answers and terms so -2π, 0, 2π and then our last part, what are the X intercepts of F? Choose the correct answer. Well, once again, going back to our graph, our X intercepts are every time we cross the X axis. So when we look here, we can see that it's going to be π halves, three Pi halves. If I labeled all these other points, we'd have negative π halves and -3 Pi halves. So in between each of these intercepts is a full π. So one way to write it would be π halves plus K π. So when we come back to our solution, let's see what it says, says, oh, so Pi halves K π, it's not going to be K Pi, it's not going to be two K π. So this would be a negative π halves, and this would be AK π. This would be a negative π halves and this would be a K π half. So it's got to be that one. This is just a different way of writing it. But if we look at this, we can see that that's really the same thing as what we said a minute ago. So if we had had X equal π halves plus K Pi, we could have shifted it over one by letting the K be a -1 if we had wanted to. So X could have been negative π halves plus K Pi. When we think about this, if we took each of them divided by two, two K / 2 -, 1 / 2 and that's all times π. So we'd get K * π - π halves where K is in the integer.