• We are asked to determine the domain and range of the given function. The domain is a set of all possible inputs and because we have a function of X, we can say the domain is a set of all possible X values, and the range is a set of all possible outputs which are the Y values or function values. Notice we are given a square root function, so the most important thing to remember here is that when we have a square root function the radicand or the number under the square root must be non-negative. Because if it was negative, we would have an imaginary number. So…

• • – WE WANT TO DETERMINE THE DOMAIN AND RANGE OF THE FUNCTION F(X)=SQUARE ROOT OF 2X – 4. THERE’S A COUPLE WAYS OF DOING THIS BASED UPON HOW MUCH WE KNOW ABOUT A GIVEN FUNCTION. IF YOU’RE MORE OF A VISUAL PERSON, THE BEST THING TO DO IS GRAPH THE FUNCTION AND THEN DETERMINE THE DOMAIN AND RANGE BY ANALYZING THE GRAPH. LET’S START BY DOING THAT AND THEN WE’LL USE A SECOND METHOD TO DETERMINE THE DOMAIN AND RANGE. SO WHETHER YOU MAKE A GRAPH USING TECHNOLOGY OR THE TABLE OF VALUES, THE GRAPH WOULD LOOK LIKE THIS. REMEMBER THE DOMAIN IS A SET OF ALL POSSIBLE X VALUES…

• – WE’RE GIVEN F OF X EQUALS THE SQUARE ROOT OF THE QUANTITY (2X – 1) – 3. WE WANT TO DETERMINE THE DOMAIN AND RANGE OF THE GIVEN FUNCTION AND THEN FIND THE INVERSE FUNCTION. BECAUSE OUR FUNCTION CONTAINS A SQUARE ROOT IN ORDER FOR THE FUNCTION VALUE TO BE REAL THE NUMBER UNDERNEATH THE SQUARE ROOT OR THE RADICAND WHICH IN THIS CASE 2X – 1 CAN’T BE NEGATIVE WHICH MEANS 2X – 1 MUST BE GREATER THAN OR EQUAL TO ZERO. SINCE 2X – 1 MUST BE GREATER THAN OR EQUAL TO ZERO THIS RESTRICTION WILL HELP US FIND OUR DOMAIN. WE JUST NEED TO SOLVE THIS…

• PROFESSOR: Hey, we’re back. Today we’re going to do a singular value decomposition question. The problem is really simple to state: find the singular value decomposition of this matrix C equals [5, 5; -1, 7]. Hit pause, try it yourself, I’ll be back in a minute and we can do it together. All right, we’re back, now let’s do it together. Now, I know Professor Strang has done a couple of these in lecture, but as he pointed out there, it’s really easy to make a mistake, so you can never do enough examples of finding the SVD. So, what does the SVD look like? What do we want to…

• HELLO again. PreCalc lesson number four of the day or something like that. So let’s talk about determining the domain of a function without the use of a graphing calculator. Now domain is the x’s that a graph can take on. Well, equations makes those graphs. If you want to find domain without the, let’s call it a crutch of a graphing calculator, you need to look at the equation itself. There is really only two problems or issues when you are looking for the domain of an algebraic equation or function. Now unless of course you are talking about trig functions which are a whole different story. That is…

• – WE WANT TO FIND THE DOMAIN OF THE SQUARE ROOT FUNCTION F OF X=THE SQUARE ROOT OF THE QUANTITY -X SQUARED + 4X + 5. THE DOMAIN OF THE FUNCTION WILL BE THE SET OF ALL POSSIBLE INPUTS OR ALL POSSIBLE X VALUES IN THIS CASE. WHEN CONSIDERING THE SQUARE ROOT FUNCTION, WE NEED TO RECOGNIZE THAT THE RADICAND OR THIS EXPRESSION UNDERNEATH THE SQUARE ROOT CANNOT BE NEGATIVE, OTHERWISE THE FUNCTION VALUE WOULD NOT BE REAL. SO OUR RESTRICTION IS THIS QUANTITY HERE MUST BE GREATER THAN OR EQUAL TO ZERO. SO BY SOLVING THIS QUADRATIC INEQUALITY, WE’LL BE DETERMINING THE DOMAIN OF OUR FUNCTION. SO TO DETERMINE…

• [MUSIC] So, before we talk about the domain of the square root function, we just want to remind ourselves what the square root function even is. So here, I’ve made a graph of the square root function. And along the x-axis, I plot the numbers one to sixteen and in the y-axis I’ve got the numbers one through four. And then in this green curve here, I’ve plotted the the, the square root function. What is the square root, right? Well, here’s an example. Here, I’ve got the square root of four. And I’m saying the square root of four is two. What that means, is if I take the…