Use the power of algebra to understand and interpret points and lines (something we typically do in geometry). This will include slope and the equation of a line.
Algebra: Graphs, graphing equations and inequalities. Algebra.Com is a people's math website. It relies on volunteers like you, who create our free content. Function Graphing Calculator. Function. y = f(x) = + More Functions. Graph. The calculator follows the standard order of operations taught by most algebra books. A graphing calculator (also graphics / graphic calculator) is a handheld calculator that is capable of plotting graphs, solving simultaneous equations, and performing. Graphing Linear Equations. Now that we have solved equations in one variable, we will now work on solving equations in two variables and graphing equations on.
Algebra - Graphing. Can you help me with a problem/homework/etc?
Show Answer Short Answer : No. Long Answer : No.
Long Answer with Explanation : I'm not trying to be a jerk with the previous two answers but the answer really is "No". Here's why. My first priority is always to help the students who have paid to be in one of my classes here at Lamar University (that is my job after all!). I also have quite a few duties in my department that keep me quite busy at times. All this means that I just don't have a lot of time to be helping random folks who contact me via this website. I would love to be able to help everyone but the reality is that I just don't have the time. So, because I can't help everyone who contacts me for help I don't answer any of the emails asking for help.
Also, when I first started this site I did try to help as many as I could and quickly found that for a small group of people I was becoming a free tutor and was constantly being barraged with questions and requests for help. Unfortunately there were a small number of those as well that were VERY demanding of my time and generally did not understand that I was not going to be available 2.
I really got tired of dealing with those kinds of people and that was one of the reasons (along with simply getting busier here at Lamar) that made me decide to quit answering any email asking for help. So, while I'd like to answer all emails for help, I can't and so I'm sorry to say that all emails requesting help will be ignored. Where are the answers/solutions to the Assignment Problems? Show Answer. Answer/solutions to the assignment problems do not exist. Those are intended for use by instructors to assign for homework problems if they want to. Having solutions (and for many instructors even just having the answers) readily available would defeat the purpose of the problems.
Please do not email asking for the solutions/answers as you won't get them from me. How do I download pdf versions of the pages? Show Answer. There are a variety of ways to download pdf versions of the material on the site. From Content Page. If you are on a particular content page hover/click on the "Downloads" menu item. You will be presented with a variety of links for pdf files associated with the page you are on.
Included in the links will be links for the full Chapter and E- Book of the page you are on (if applicable) as well as links for the Notes, Practice Problems, Solutions to the Practice Problems and Assignment Problems. The links for the page you are on will be highlighted so you can easily find them. From Download Page. All pdfs available for download can be found on the Download Page. Links to the download page can be found in the Download Menu, the Misc Links Menu and at the bottom of each page. Once on the Download Page simply select the topic you wish to download pdfs from. This will present you with another menu in which you can select the specific page you wish to download pdfs for.
Once you have made a selection from this second menu up to four links (depending on whether or not practice and assignment problems are available for that page) will show up below the second menu that you can click on to initiate the download. From Site Map Page. The Site Map Page for the site will contain a link for every pdf that is available for downloading. You can access the Site Map Page from the Misc Links Menu or from the link at the bottom of every page. Note for Internet Explorer Users.
If you are using Internet Explorer in all likelihood after clicking on a link to initiate a download a gold bar will appear at the bottom of your browser window that will allow you to open the pdf file or save it. I've found a typo in the material.
Show Answer. If you have found a typo or mistake on a page then please contact me and let me know of the typo/mistake. Please be as specific as possible in your report. Let me know what page you are on and just what you feel the typo/mistake is. It's kind of hard to find the potential typo if all you write is "The 2 in problem 1 should be a 3" (and yes I've gotten handful of typo reports like that..). Some of the equations are too small for me to see!
Show Answer. This is a problem with some of the equations on the site unfortunately. It is especially true for some exponents and occasionally a "double prime" 2nd derivative notation will look like a "single prime". You can click on any equation to get a larger view of the equation. Clicking on the larger equation will make it go away. If you are a mobile device (especially a phone) then the equations will appear very small. I am attempting to find a way around this but it is a function of the program that I use to convert the source documents to web pages and so I'm somewhat limited in what I can do. I am hoping they update the program in the future to address this.
In the mean time you can sometimes get the pages to show larger versions of the equations if you flip your phone into landscape mode. Another option for many of the "small" equation issues (mobile or otherwise) is to download the pdf versions of the pages.
These often do not suffer from the same problems. Is there any way to get a printable version of the solution to a particular Practice Problem? Show Answer. Yes. If you want a printable version of a single problem solution all you need to do is click on the "[Solution]" link next to the problem to get the solution to show up in the solution pane and then from the "Solution Pane Options" select "Printable Version" and a printable version of that solution will appear in a new tab of your browser. In this section we need to review some of the basic ideas in. It is assumed that you’ve seen.
We will only be reviewing some of. We will start off with the Rectangular or Cartesian. This is just the. Here is the Cartesian coordinate system with. The horizontal and vertical axes, typically called thex- axis. In each. quadrant we have the following signs for x. Each point in the coordinate system is defined by an ordered pair of the form . The first number listed is the x- coordinate.
The ordered pair for any given. The point where the two axes cross is called the origin and has the coordinates . Note as well that the order of the coordinates is. For example, the point is the point that is two units to the right of. We now need to discuss graphing an equation. The first question that we should ask is what. A. graph is the set of all the ordered pairs whose coordinates satisfy the equation. For instance, the point is a point on the graph of while isn’t on the graph. How do we tell this? All we need to do is take the coordinates of the. Let’s do that for both to verify the claims.
In this case we have and so plugging in gives, So, the coordinates of this point satisfies the equation and. Here we have and . Plugging these in gives, The coordinates of this point do NOT satisfy the equation. Now, how do we sketch the graph of an equation? Of course, the answer to this depends on just. For instance, if you know that the equation. There are also many other kinds. We will see many of these in. However, let’s suppose that we don’t know ahead of time just.
In these cases we will need to recall that. So, all we can do is plot points. We will pick values of x, compute y from the. How, do we determine which values of x to choose? Unfortunately. We pick. some values and see what we get for a graph.
If it looks like we’ve got a pretty good sketch we stop. If not we pick some more. Knowing the values of x to choose is really something that we can only get with. Hopefully, by the end of this course you will. Let’s take a quick look at a graph. Example 1 Sketch. Solution. Now, this is a parabola and after the next chapter you. However, we haven’t gotten that far yet and. As mentioned earlier, it helps to have an idea of what.
So, don’t worry at this. After the next chapter you would also be able to choose these values. Here is a table of values for this equation. Let’s verify the first one and we’ll leave the rest to you. For the first one we simply. Here is the graph of this equation.
Notice that when we set up the axis system in this example. For. example, since we didn’t go past - 2 with our computations we didn’t go much. Also, notice that we used a different scale on each of the. With the horizontal axis we. This will often be done in order to make the. The final topic that we want to discuss in this section is.
Notice that the graph in the above example. All three of these points are called. We can, and often will be. We often will want to know if an intercept crosses the x or y- axis. So, if an intercept.
Likewise, if an intercept crosses the y- axis we will call it a y- intercept. Now, since the x- intercept. Also, the x. coordinate of the y- intercept will be.
These facts give us a way to determine the. To find the x- intercepts for an equation all that we.
Likewise to find the y- intercepts for an equation we simply. Let’s take a quick look at an example.
Example 2 Determine. Solution](b) [Solution](c) [Solution]Solution.
As verification for each of these we will also sketch the. We will leave. the details of the sketching to you to verify. Also, these are all parabolas and as mentioned. Let’s first find the y- intercept(s). Again, we do this by setting and solving for y. This is usually the. So, let’s find the y- intercept(s). So, there is a single y- intercept.
The work for the x- intercept(s). Here is that work. For this equation there are two x- intercepts : and . Oh, and you do remember how to solve quadratic equations right? For verification purposes here is sketch of the graph for. Return to Problems](b) First, the y- intercepts. So, we’ve got a single y- intercepts. Now, the x- intercept(s). Okay, we got complex solutions from this equation. What this means is that we will not have.