2018年5月5日 · The last one A function has to return a unique value when given an argument. In the last set {(–2, 1), (3, –4), (–2, –6)}, the argument -2 is supposed to return both 1 and -6 : this is not possible for a function. Additional technical points There is another important part of the definition of a function that we should really worry about here. A function is defined with a …

2018年6月26日 · See explanation below A function is an aplication from a set A to other B such that, very element from A has a unique "associated" element by function. In first case: There is an element (3), with 2 arrows, so this element has no unique element in y. Is not a function Second case: there are 2 pairs (-1,-11) and (-1,-5) saying that element -1 has 2 associates by function. …

2018年3月5日 · # "We are asked to decide if it defines a function." # # "If no matter what the value of the first variable," \ x, "there is" # # "precisely one value of the second variable," \ y, "connected" # # "to it inside the relationship -- then it will be a function. If this" # # "breaks down for even one value of the first variable, it will fail" #

2015年11月13日 · This is the equation of a circle of radius 4 with centre (0, 0). If you attempt to define y in terms of x you get multiple values for x in (-4, 4). Starting with x^2+y^2=16, subtract x^2 from both sides to get: y^2 = 16-x^2 Then taking square roots of both sides: y = +-sqrt(16-x^2) = +-sqrt(4^2-x^2) Now sqrt(4^2-x^2) only takes Real values when 4^2-x^2 >= 0, that is when …

2015年11月1日 · A relation is a function if for every x there is (at most) one y. A function can be seen as a recipe, saying if x is such, then y is so. In this case the relation can be rewritten as y^2=25-x^2->y=+sqrt(25-x^2)ory=-sqrt(25-x^2) These values are only defined in the domain -5<=x<=5, but that's not important here: For the x's in the domain there are always TWO y's …

2015年4月6日 · For graphing an exponential function, basically three things have to be observed. First is the end behavior of the function. One should be able to figure out what happens when x goes to +infy and what happens when x goes to - infy. Next is the point at which the graph would crosss y -axis, that is when x=0.

2015年8月1日 · x^2+y^2 = 9 is not a function In order for an equation to represent a function any single value of x must have at most one corresponding value of y which satisfies the equation.

What cosine function represents an amplitude of 3, a period of π, no horizontal shift, and a vertical shift of? How do you find the amplitude and period of a function y=-5 cos 6x? How would you convert f(x) = 20sin(π/6(t)) + 4 into a cosine function?

2017年3月25日 · No - there is more than one y value for each x value in the domain. Equations in the form of ax^2+by^2=r^2 form circles. x^2+y^2=4=2^2 looks like this: graph{x^2+y^2-4=0 [-7.023, 7.024, -3.51, 3.513]} Is this a function? That is, does there exist a single y value for each x value in the domain? And the answer is no - for essentially all the x values (excepting x=pm2), …

2018年6月24日 · The very first graph represents the graph of f. I assume you meant f(x)=log_2 x +1 First of all, we see that this function is concave. Basically, any line segment that connects two points on the graph will be below the graph itself. This already eliminates the two right options. When we want to graph a function, finding its roots is most useful. The roots are solutions of …