![]() ![]() In such cases, other measures such as variance and standard deviation may be used to provide a more comprehensive understanding of the data. ![]() In some cases, the range may not provide a complete picture of the data as it only takes into account the largest and smallest values. Therefore, the range of this set is 15-3=12. For example, if a set of numbers is, the largest number is 15 and the smallest number is 3. Range can be calculated by subtracting the smallest number from the largest number in a set. The range is an important concept in mathematics as it helps in determining the spread of the data and provides an insight into the variability of the data. ![]() It is the difference between the largest and smallest numbers in a set or sequence. In mathematics, range refers to the set of all output values of a function. Of 20.408 m, then h decreases again to zero, as expected.Understanding the definition of range in math `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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