In Precalculus we study many topics which are Sets, real Numbers, complex numbers, composite and polynomial Functions, trigonometry, limits, vectors, metrics, conic section, logarithm function, basic graphs, binomial theorem, mathematical induction, sequence, series, roots and Rational Exponents, quadratic Functions, inverse functions, inequality involving Rational functions, Algebraic simplification and many more. Here we will discuss precalculus functions. First we will discuss about functions?
If one object or thing is depends on the other, for example we can say that Area of a Circle depends on the Radius of Circle, it Mean that when the radius of circle changes then the area of circle also changes. In the same way relationship between two variables that is ‘u’ and ‘v’ is known as function. A rule which defines for each value of ‘u’ and ‘v’ then in this types of case generally; ‘v’ is a function of u.
Thus, we can say that a function must be single-valued function. For example,
v = 2u + 3. For every value u there is a unique value of v.
Here the value of u is known as the domain of the function. These are the values for which the function is defined.
In the given function v = 2u + 3, the Domain may include all the real number ‘u’ may be any real number and the domain may be arbitrarily classified.
Once the domain is defined for a function then the values of ‘v’ that correspond to the values of ‘u’ are known as The Range of a function. This is all about pre Calculus functions.
Function is a relation between Set of inputs and set of outputs in which every value of input is related to exactly one value of output. In a function, every input value provides exactly one output value. It is generally written as f (a) where ‘a’ is the value you assign it. Suppose f (a) = a / 4 (f of ‘a’ is ‘a’ divided by 4") is a function, because for every value of ‘a’...Read More
In mathematics, function is used to show the relationship between values. Each input values of a function gives back exactly one output value. It is basically written as f (s) where‘s’ is the value you assign it. Like, f (s) = s / 2 (f of s is s divided by 2") is a function, because for every value of "s" you get another value "s / 2". So:
⇒ f (2) = 1,
* f(4) = 2,
* f...Read More
Domain of a function can be defined as all possible values of ‘x’ coordinate. Range of a function is equals to possible values of ‘y’ coordinates. Suppose we have some values (13, -56), (-38, 47), (75, -99), (-65, 19).
Then Domain of function is ‘x’ coordinate values. So domain = 13, -38, 75, -65 and range is ‘y’ coordinate values, so range = -56, 47, -97...Read More
Root Functions are basically the functions that have their resultant range always greater than or equals to 0. If range values go below 0, they will become imaginary and it is impossible to practically deal with imaginary Numbers. So, domain and range of a root function can be explained by example:
Example: Find the Domain and range of function giv...Read More
Trigonometric function is defined as the branch of mathematics which deal with angles and sides of a Right Angle triangle. Right angle triangle consists of a base, perpendicular and hypotenuse and depending on these three parameters six Trigonometric Functions are there termed as Sine function, Cosine function, tangent function, cotangent function, Se...Read More
Radical Numbers are the numbers which are written under symbol of radical √. For Example: √x is a radical number. Every number has certain range and Domain. Let us see domain and range of a radical function.
Radical function is defined as as a function which has at least one radical term in the function. For example √(x - 8) is a radical function....Read More
Functions are actually used to explain the relationship between two or more variables. These relationships between various variables involve independent values and inputs and also dependent values and outputs. Dependent values and outputs are those variables which are obtained from independent values. The Domain of a relation can be defined as...Read More
Function can be defined as a mathematical relation that is used to describe the relationship between inputs and outputs. Relations between inputs and outputs are actually the Relations between independent (inputs) and dependent (outputs) values. We know that outputs are dependent on inputs that’s why they may also been referred as dependent varia...Read More
Set values of inputs is known as Domain of function and Set of corresponding outputs is known as range of function. Here we will understand how to find Domain and Range of a relation Function. Steps to be followed for calculation of domain and range of given relation function are shown below:
Step 1: To calculate domain and range of a relation fi...Read More
If there is function f(x) = x then reciprocal of this function will be 1 / x. This is a reciprocal function. Let us see how to find Domain and range of a reciprocal function.
We can understand range and domain of reciprocal function by taking an example but before that let us understand domain and thee range of a function.
Parabola is a kind of conic section formed by Intersection of plane and cone. Parabolic graph can open in either upward or downward direction. Point vertex is described as the Point in parabolic graph on which Parabola opens up or down. Parabolic graph is always symmetrical to axis whether it is x-axis or y-axis. Parabola has a Quadratic Equation in form "...Read More