![]() y = x²).Ī function is odd if the sign of the function is changed when x is replaced by -x. Even functions which are polynomials have even degrees (e.g. The graph of such a function will be symmetrical in the y-axis. An example of a discontinuous graph is y = 1/x, since the graph cannot be drawn without taking your pencil off the paper:Ī function is periodic if its graph repeats itself at regular intervals, this interval being known as the period.Ī function is even if it is unchanged when x is replaced by -x. A function is continuous if its graph has no breaks in it. This video explains more about the inverse of a functionįunctions can be graphed. Note that the graph of f -1 will be the reflection of f in the line y = x. The inverse is said to exist if and only there is a function f -1 with ff -1(x) = f -1f(x) = x To find the inverse of a function, swap the x"s and y"s and make y the subject of the formula.į -1(x) is the standard notation for the inverse of f(x). For example the inverse of y = 2x is y = ½ x. The inverse of a function is the function which reverses the effect of the original function. Sometimes, fg is written as fogĪs you can see, fg does not necessarily equal gf On a graph, a function is one to one if any horizontal line cuts the graph only once.įg means carry out function g, then function f. f(x) = x 2 is not one to one because, for example, there are two values of x such that f(x) = 4 (namely –2 and 2). We say that a function is one-to-one if, for every point y in the range of the function, there is only one value of x such that y = f(x). The range is all of the real numbers greater than (or equal to) zero, since if y = x 2, y cannot be negative. So if y = x 2, we can choose the domain to be all of the real numbers. The range of the function is the set of all values that the function can take, in other words all of the possible values of y when y = f(x). The domain of a function is the set of values which you are allowed to put into the function (so all of the values that x can take). y = f(x) ), then the value of y when x is 4 is f(4), which is found by replacing x"s by 4"s. If f(x) = 3x, and y is a function of x (i.e. The phrase "y is a function of x" means that the value of y depends upon the value of x, so: The same notion may also be used to show how a function affects particular values.į(4) = 4 2 + 5 =21, f(-10) = (-10) 2 +5 = 105 or alternatively f: x → x 2 + 5. The Function which squares a number and adds on a 3, can be written as f(x) = x 2+ 5. A function may be thought of as a rule which takes each member x of a set and assigns, or maps it to the same value y known at its image.Ī letter such as f, g or h is often used to stand for a function.
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