![]() 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.) In a set of data, the range is the difference between the greatest and smallest value. ![]() (This makes sense if you think about throwing a ball upwards. In math, range is a statistical measurement of dispersion, or how much a given data set is stretched out from smallest to largest. 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. 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`. Swift has reportedly turned that gig down twice.Need a graphing calculator? Read our review here: The star-studded event will also feature pregame performances by Reba McEntire, Post Malone and Andra Day, Tiesto as the first-ever " in-game DJ" and a halftime show headlined by Usher. "And they have sort of stumbled into this hyper-influencer who's doing a lot of that work for them really well."Ī Swift Super Bowl appearance would all but guarantee a huge boost in ratings, with Poynter reporting that it has the chance to become the most-viewed U.S.-based telecast of all time (even if she's only seen in brief glimpses, which a recent New York Times analysis confirmed has so far been the case). "The NFL for years and years has been trying to court women and court more women fans, and to be frank, they haven't always been very good at it," she added. Swift isn't just bringing the NFL more viewers, but a whole new - and decidedly more feminine - demographic of fans, Princiotti noted. Pop Culture Happy Hour A match made in fandom: Travis, Taylor and the weirdness of celebrity relationships
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