Of 20.408 m, then h decreases again to zero, as expected. `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. Range, which is the difference between the largest and smallest value in the data set, describes how well the central tendency represents the data. 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.
#RANGE MATH EXAMPLE HOW TO#
For a more advanced discussion, see also How to draw y^2 = x − 2. We saw how to draw similar graphs in section 4, Graph of a Function.This indicates that the domain "starts" at this point. The enclosed (colored-in) circle on the point `(-4, 0)`.This will make the number under the square root positive. The only ones that "work" and give us an answer are the ones greater than or equal to ` −4`.
To see why, try out some numbers less than `−4` (like ` −5` or ` −10`) and some more than `−4` (like ` −2` or `8`) in your calculator. The domain of this function is `x ≥ −4`, since x cannot be less than ` −4`. Need a graphing calculator? Read our review here:
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