When choosing a domain and range calculator, user experience is paramount. Some popular websites include:Ī) Wolfram Alpha – It’s an online computational knowledge engine that provides specialized tools for calculating the domain and range of functions.ī) Symbolab – This user-friendly website offers step-by-step solutions along with the domain and range calculator feature.Ĭ) Desmos – Known for its interactive graphing calculator, Desmos can also be used to find the domain and range of different functions. ![]() There are many websites offering free domain and range calculators with various features that can cater to different needs. For instance, you may need a tool that is specifically designed for high school math courses or one that caters to advanced mathematics like multivariable calculus or linear algebra. This article focuses on finding the perfect calculator to suit your needs.īefore searching for a suitable domain and range calculator, you must understand your educational or professional requirements. Finding the domain and range of a function can be challenging, but fortunately, there are numerous domain and range calculators available online to simplify the process for you. Of 20.408 m, then h decreases again to zero, as expected.The concept of domain and range is an essential part of mathematics, involving the set of all possible input values (domain) and their corresponding output values (range). `t = -b/(2a) = -20/(2 xx (-4.9)) = 2.041 s `īy observing the function of h, we see that as t increases, h first increases to a maximum What is the maximum value of h? We use the formula for maximum (or minimum) of a quadratic function. It goes up to a certain height and then falls back down.) (This makes sense if you think about throwing a ball upwards. We can see from the function expression that it is a parabola with its vertex facing up. So we need to calculate when it is going to hit the ground. Also, we need to assume the projectile hits the ground and then stops - it does not go underground. Generally, negative values of time do not have any Have a look at the graph (which we draw anyway to check we are on the right track): So we can conclude the range is `(-oo,0]uu(oo,0)`. We have `f(-2) = 0/(-5) = 0.`īetween `x=-2` and `x=3`, `(x^2-9)` gets closer to `0`, so `f(x)` will go to `-oo` as it gets near `x=3`.įor `x>3`, when `x` is just bigger than `3`, the value of the bottom is just over `0`, so `f(x)` will be a very large positive number.įor very large `x`, the top is large, but the bottom will be much larger, so overall, the function value will be very small. As `x` increases value from `-2`, the top will also increase (out to infinity in both cases).ĭenominator: We break this up into four portions: ![]() To work out the range, we consider top and bottom of the fraction separately. So the domain for this case is `x >= -2, x != 3`, which we can write as `[-2,3)uu(3,oo)`. ![]() (Usually we have to avoid 0 on the bottom of a fraction, or negative values under the square root sign). In general, we determine the domain of each function by looking for those values of the independent variable (usually x) which we are allowed to use. For a more advanced discussion, see also How to draw y^2 = x − 2.
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