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Why is WebGraphing.com easier to use than a standard graphing calculator?
How do I become a Member?
What are the benefits of membership?
What is the difference between the basic, intermediate and advanced graphing calculators?
Are there any special syntax requirements?
Why would I generate a random graph?
Why does the graph change color when I roll over it?
What are the benefits of seeing color-coded graphs?
What happens to the color coding for straight lines?
Aside from color-coding, what other “important mathematical features” are included in the graph?
What is Smart Zooming?
Are there any other unique features on WebGraphing.com?
Can I graph any function?
Can I print out the graphs and solutions?
How do I use The Analyzer?
What are Tricks of the Trade?
How do I post to the forum?
What is Guess the Graph?

click any below to return to the questions list

Why is WebGraphing.com easier to use than a standard graphing calculator?

To graph a function using a standard graphing calculator, you need to select a viewing window—the plotting interval and range—guessing at values you hope will include all the important mathematical features. This may require several tries, and there is no guarantee that your final graph includes everything. WebGraphing.com does not require trial and error. It uses behind-the-scenes mathematical analyses to automatically select a viewing window that includes all the important mathematical features. After seeing the “complete graph,” you can graph again with a viewing window of your own choosing or use Smart Zooming to focus on a particular interval and minimize the guesswork..

How do I become a Member?

Becoming a Member is free and easy: just fill out the registration form and respond to the confirming email that WebGraphing.com sends to you. Membership is open to students, teachers, and parents of math students.

A+ membership is by subscription, but you must first become a Member. There are several ways to become an A+ Member. Whether you just want to study for an upcoming test, get material for a math project, or use it for a whole semester or year, there are subscription periods as short as 2 days and as long as a year.

 What are the benefits of membership?

Membership entitles you to: (1) complete graphs of all polynomials of degree less than 4, (2) detailed analyses explaining the mathematics that produces the complete graphs, (3) access to post and respond to questions on the forum, and (4) our Tricks of the Trade for graphing polynomials. In addition, you can sample premium content: complete graphs with analyses for any functions.

A+ membership entitles you all the benefits of membership plus: (1) complete graphs of all mathematical functions studied in algebra, precalculus, and first year calculus, (2) detailed analyses explaining the mathematics that produces the complete graphs, (3) priority in getting homework questions answered on the forum by a WebGraphing.com moderator (mathematician, math teacher, or math professor), and (4) our Tricks of the Trade for graphing rational, algebraic, and transcendental (nonalgebraic) functions.

What is the difference between the basic, intermediate and advanced graphing calculators?

The Basic Calculator keypad is designed for algebra and beginning precalculus students so as not to intimidate budding “apprentice mathematicians” with unnecessary jargon. It can be used to enter any arithmetic combination of expressions in x as well as powers of x, using the power symbol ^ (as in x^2, read x squared).  Each of the basic, intermediate and advanced keypads can be used interchangeably with your computer keypad to enter any function, including functions on one of the other keypads. Note that when you click the π key, the letters “pi” are entered; alternatively you can type “pi” to enter the symbol π.

The Intermediate Calculator keypad additionally has 5 function keys for convenience in entering “named” functions that students first meet: square root, absolute value, natural logarithms, logarithms to any base, and exponential functions. Note that when you click any of these function keys, say log, the letters with opening left parenthesis “log(“ are automatically entered for your convenience.  After entering the argument, say 2x+1, you must also enter the closing right parenthesis, “)”, to keep parentheses paired off, so the final entry reads: log(2x+1).

The Advanced Calculator keypad additionally has all six trig functions and their inverses as well as all six hyperbolic trig functions and their inverses. Note that when you click, say, the inverse sine key, sin-1, the letters with left parenthesis "arcsin(" are entered. Inserting the letters “arc” in front of any trig or hyperbolic trig function is the traditional way of referring to the corresponding inverse function.

Are there any special syntax requirements?

When you click, say, the sqrt key, the letters entered are “sqrt(“; that is, the function name is entered together with the left parentheses.  You need to enter the argument, say, x+1, followed by the right parentheses, “x+1)” so it finally reads: sqrt(x+1).  Entering “sqrtx+1” would produce the response: “Oops! Syntax Error.”  Even if the argument is simply “x”, our syntax requires that parentheses be used: sqrt(x).

To enter a root function, say the cube root of x, you need to write it using the power operator, ^, with a fractional exponent enclosed in parentheses: x^(1/3). As a consequence, there are two way to enter the square root of x: sqrt(x) or x^(1/2). 

Note that the log key refers to the logarithm of x to the base e.  If you want to refer to another base, say 5, you would type “log(5,x)”.  It is for this reason that, log(x) can be used interchangeably with log(e,x) and ln(x).

To minimize syntax errors, you can use any of the onscreen keypads .  For example, to graph the inverse tangent of x, if you click the inverse tangent key, tan-1, you will see “arctan(“ entered for you in the entry field after “y=”.  You can complete the entry by typing “x)” so the final entry reads: arctan(x).  Also, when you click the key for the exponential function, ex, you will see “e^(“ in the entry field.  Again, you need to enter the argument, say x, followed by the closing right parenthesis so it reads: e^(x).

Why would I generate a random graph?

This is a quick way for a visitor to get a live sample of what the web site has to offer. When a visitor clicks the generate a random graph button, WebGraphing.com returns a complete graph of a randomly generated polynomial function up to degree 3 along with descriptive answers in The Analyzer that explain the mathematics needed to produce the graph by hand. A visitor will see that by rolling over the graph, it turns from red and blue, which highlight segments where the graph is increasing or decreasing, to green and purple, which highlight segments where the graph is concave up or concave down. In addition, a visitor can explore the breadth of mathematical coverage and the details that the descriptive answers provide in The Analyzer.

When a Member clicks the generate a random graph button, WebGraphing.com returns a complete graph of a randomly generated polynomial function up to degree 5 along with descriptive answers in The Analyzer that explain the mathematics needed to produce the graph by hand.  This is a quick way to explore a number of live higher degree polynomials—what they look like and their various properties.

When an A+ Member clicks the generate a random graph button, depending on the level of graphing calculator selected, WebGraphing.com returns a complete graph of a randomly generated elementary, intermediate or advanced function with descriptive answers in The Analyzer that explain the mathematics needed to produce the graph by hand. This is a convenient way to explore various live intermediate-level and advanced mathematical functions—what they look like and their various properties.

Why does the graph change color when I roll over it?

To aide visualization, when you move your cursor over your graph, it changes from red and blue to purple and green, where purple highlights the concave up curve segments and green highlights the concave down curve segments.

 What are the benefits of seeing color-coded graphs?

In addition to aiding your visualization of the increasing/decreasing segments and concave up/concave down segments, the color coding serves the purpose of identifying turning points and points of inflection even when a curve appears flat in a certain region.  You can be sure that if a curve is flat but has both red and blue meeting at a juncture, there is a turning point at the juncture.  In our Rational Examples, see the case of the “hidden” turning point.  This “hidden” turning point can be revealed on resizing in the vicinity of the juncture of the two colors, most conveniently by using Smart Zooming.  The same can be said for “hidden” changes in concavity.  If a curve appears flat in a certain region that includes the juncture of green and purple colors, despite the appearance of being flat, the shape of that curve is changing concavity at the juncture and it may be possible to confirm this visually by resizing the graph in the vicinity of the juncture.

 What happens to the color coding for straight lines?

Straight lines are colored red when they are increasing, blue when they are decreasing, and black when they are horizontal since a horizontal line is neither increasing nor decreasing. Also, since straight lines are neither concave up nor concave down, when you move your cursor over the graph, the line is colored black to signify the absence of concavity.

 Aside from color-coding, what other “important mathematical features” are included in the graph?

Certain functions have breaks, discontinuities, and asymptotic behaviors, which all good math textbooks illustrate by using dashed lines and small empty or filled circles. The illumination of these important mathematical features is an invaluable addition to a graph, required to visually identify the special attributes of a function. WebGraphing.com automatically includes these features in its graphs, while standard graphing calculators do not.

 What is Smart Zooming?

After seeing the complete graph, if you enter only the lower (Xmin) and upper (Xmax) bounds on the x-values and click the Graph Again button, Smart Zooming takes over and WebGraphing.com automatically determines optimal lower (Ymin) and upper (Ymax) bounds for the y-values; the resulting viewing window includes all the important mathematical features on your selected interval (Xmin,Xmax). This is convenient and more powerful than ordinary proportional zooming since you don’t have to go through trial and error to get an optimal graph. Of course, you can enter your own lower (Ymin) and upper (Ymax) bounds on the y-values and click the Graph Again button to resize the graph to your own liking. In fact, you can do this repeatedly.

Are there any other unique features on WebGraphing.com?

Whenever feasible, in our descriptive answers we give exact numbers, like the ones you get solving equations longhand when you are not using a calculator. For example, if we have an equation to solve, say x2 = 2, we give the exact (“symbolic” is the technical jargon) answer x = ± . We also give the approximate value x = ±1.41 to two decimal places. When the exact value is not too lengthy, you can expect to see the exact value. This feature—giving both exact and approximate answers—helps to make connections between symbolic values and their magnitude.

 Can I graph any function?

WebGraphing.com is designed to analyze and graph functions typically found in math textbooks, from algebra through precalculus and first-year calculus. We tested our comprehensive graphing system with graphing problems from eight calculus textbooks and it handled all these problems successfully. Of course, some advanced functions can take longer to analyze and graph and WebGraphing.com is not designed to spend an inordinate amount of time with any particular function. For such advanced functions, when analysis takes too long, we deliver one or both graphs in black with whatever analyses were possible within the time constraints.  If you come across a function for graphing in your math textbook that you believe was not handled properly, please put it out on our forum (mention the title, author, edition, and page number for reference) so we can investigate it.  We aim to improve.

 Can I print out the graphs and solutions?

Yes, you can use your browser’s print button to print out any information on the web site. Also, you can right click on any graph and save the graph to your computer as a picture that can subsequently be inserted into your document. Teachers can use this feature for inserting graphs into their test questions.  Students can use this feature for inserting graphs into their math projects.

 How do I use The Analyzer?

In general, algebra and precalculus students will be most interested in the analyses on the left side of The Analyzer pad while calculus students will be most interested in the analyses on the right side of The Analyzer pad.  Clicking on, say, the Intercepts button will give details about x- and y-intercepts and how to find them.  Clicking the Show All Analyzer Solutions button will enable you to see all the details at once.  The latter can also be printed, together with the graph, for offline reference and study.

 What are Tricks of the Trade?

The Tricks of the Trade web page offers practical advice for graphing functions by specific category: polynomial functions, rational functions, algebraic functions, and transcendental (nonalgebraics) functions. It provides useful information for developing both an overview of properites specific to each type plus pinpointed advice on what to look for.

 How do I post to the forum?

Once you become a member, you are entitled to post questions on the forum and answer other members' questions. The forum is moderated, so moderators may, at their discretion, edit questions to improve clarity or exclude questions that are off topic. Along with other members, moderators may also answer questions.

What is Guess the Graph?

Guess the Graph is a game you can play to see how well you can spot differences between the four specific categories of graphs: polynomial, rational, algebraic, and transcendental (nonalgebraic).  Strictly speaking, polynomial functions are also rational functions and rational functions are also algebraic functions, so being specific requires careful consideration. There are over 200 graphs that are selected randomly while you play.

       

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