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Sign chart calculus khan academy1/19/2024 And we see g of negativeĤ is 2 less than that. Is f of x in red again, and here is g of x. But if you look atĮqual to f of x plus 1. Try to find the closest distance between the two. Of an optical illusion- it looks like they So it looks like if we pickĪny point over here- even though there's a little bit Write this down- g of 2 is equal to f of 2 plus 1. And we see that, at leastĪt that point, g of x is exactly 1 higher than that. Hope I didn't over explain, just proud of what I made tbh so 5*f(x) would make a point (2,3) into (2,15) and (5,7) would become (5,35)ī will shrink the graph by a factor of 1/b horizontally, so for f(5x) a point (5,7) would become (1,3) and (10,11) would become (2,11)Ĭ translates left if positive and right if negative so f(x-3) would make (4,6) into (7,6) and (6,9) into (9,9)ĭ translates up if positive and down if negative, so f(x)-8 would make the points (5,5) and (7,7) into (5,-3) and (7,-1)Īlso should note -a flips the graph around the x axis and -b flips the graph around the y axis. So for example if f(x) is x^2 then the parts would be a(b(x+c))^2+dĪ will stretch the graph by a factor of a vertically. Then if m is negative you can look at it as being flipped over the x axis OR the y axis.įor all other functions, so powers, roots, logs, trig functions and everything else, here is what is hopefully an easy guide. So negative 2 is less than orĮqual to x, which is less than or equal to 5.Yep, for linear functions of the form mx+b m will stretch or shrink the function (Or rotate depending on how you look at it) and b translates. So on and so forth,īetween these integers. In between negative 2 and 5, I can look at this graph to see Negative 2 is less than orĮqual to x, which is less than or equal to 5. What is its domain? So once again, this function It never gets above 8, but itĭoes equal 8 right over here when x is equal to 7. Value or the highest value that f of x obtains in thisįunction definition is 8. Or the lowest possible value of f of x that we get What is its range? So now, we're notįunction is defined. Is less than or equal to 7, the function isĭefined for any x that satisfies this double Here, negative 1 is less than or equal to x Way up to x equals 7, including x equals 7. So it's defined for negativeġ is less than or equal to x. This function is not definedįor x is negative 9, negative 8, all the way down or all the way What is its domain? Well, exact similar argument. Is less than or equal to x, which is less thanĬondition right over here, the function is defined. So the domain of thisĭefined for any x that is greater than orĮqual to negative 6. Wherever you are, to find out what the value of ![]() ![]() It only starts getting definedĪt x equals negative 6. It's not defined for xĮquals negative 9 or x equals negative 8 and 1/2 or Is equal to negative 9? Well, we go up here. We say, well, what does f of x equal when x Is the entire function definition for f of x. Right over here, we could assume that this What is its domain? So the way it's graphed One more point (0,6) would give 6>3 which is a true statement, and shading should include this point. ![]() If point is (1,5) you can do the same thing, 5 > 5, but this would be right on the line, so the line would have to be dashed because this statement is not true either. If you try points such as (0,0) and substitute in for x and y, you get 0 > 3 which is a false statement, and if you did it right, shading would not go through this point. So lets say you have an equation y > 2x + 3 and you have graphed it and shaded. The has to do with the shading of the graph, if it is >, shading is above the line, and ). Without the "equal" part of the inequality, the line or curve does not count, so we draw it as a dashed line rather than a solid line The "equal" part of the inequalities matches the line or curve of the function, so it would be solid just as if the inequality were not there.
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