![]() ![]() The graph may continue to the left and right beyond what is viewed, but based on the portion of the graph that is visible, we can determine the domain as \(1973≤t≤2008\) and the range as approximately \(180≤b≤2010\). (range largestnumber - smallestnumber) The mass of 7 babies are as follows: 2.5 kg, 3.1 kg, 3.4 kg, 3.5 kg, 3. The output quantity is “thousands of barrels of oil per day,” which we represent with the variable \(b\) for barrels. The range of a set of numbers is the largest value, subtract the smallest value. The input quantity along the horizontal axis is “years,” which we represent with the variable \(t\) for time. Of 20.408 m, then h decreases again to zero, as expected.\): Graph of the Alaska Crude Oil Production where the vertical axis is thousand barrels per day and the horizontal axis is years (credit: modification of work by the U.S. `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): To find the range, simply subtract the lowest value from the greatest. So we can conclude the range is `(-oo,0]uu(oo,0)`. The range is the simplest measurement of the difference between values in a data set. 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. TrueStrike’s forgiving strike surface and divot simulating subsurface. When `x=-2`, the bottom is `(-2)^2-9=4-9=-5`. TrueStrike driving range mats have a ruckable top surface and a gel-filled divot simulating subsurface which accurately recreates the effects of playing off a natural fairway by allowing the club head to play through the playing surface as it would on turf. 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: For students between the ages of 11 and 14. To work out the range, we consider top and bottom of the fraction separately. Learn how to calculate and interpret the mean, median, mode and range to find averages with this BBC Bitesize Maths article. 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`. Need a graphing calculator? Read our review here: ![]()
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