Basic Calculus Terminology Flashcards
What is a Function?
A function is a set that takes each value of an input set and relates it to each value of an output set.
“The Input set is usually called the domain and the output set is usually called the range.
What is a domain and range?
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
domain is x and range is y
What is an independant variable?
Independent variables are the “inputs” for functions. The value of an independent variable does not depend on other variables. Rather, changes in the independent variable (which take place in our “function machine”) cause a change in another variable (the dependent variable).
What is a Dependent variable?
A dependent variable is a variable that depends on one or more other variables. In calculus, the dependent variable is the output of a function. If you are given a simple formula, like y = x3, then y is a function of x (you can also say that “y depends on x.” … y is the dependent variable.
what is mathematical modeling?
Mathematical modelling is an attempt to study some part (or form) of the real-life problem in mathematical terms. Conversion of physical situation into mathematics with some suitable. conditions is known as mathematical modelling.
Example: An ice cream company keeps track of how many ice creams get sold on different days. By comparing this to the weather on each day they can make a mathematical model of sales versus weather. They can then predict future sales based on the weather forecast, and decide how many ice creams they need to make …
what is an absolute value?
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative. Take a look at some examples.
what are odd and even functions?
If a graph is symmetrical about the y- axis, the function is even. If a graph is symmetrical about the origin, the function is odd. If a graph is not symmetrical about the y-axis or the origin, the function is neither even, nor odd.
definition of increasing and decreasing?
We all know that if something is increasing then it is going up and if it is decreasing it is going down. Another way of saying that a graph is going up is that its slope is positive. If the graph is going down, then the slope will be negative.
What does Linear mean?
In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term affine function is often used.
Linearity is the property of a mathematical relationship (function) that can be graphically represented as a straight line. Linearity is closely related to proportionality. … The word linear comes from Latin linearis, “pertaining to or resembling a line”.
what does quadratic mean ?
A quadratic function (also called a quadratic, a quadratic polynomial, or a polynomial of degree 2) is special type of polynomial function where the highest-degree term is second degree
what does cubic mean ?
In geometry, cubic units can be defined as the units used to measure volume. The volume of a unit cube whose length, width and height are 1 unit each is 1 cubic unit. … Some examples of cubic units in metric units are cubic meters, cubic centimeters, and in customary units are cubic inches, cubic feet.
what does quartic mean ?
In algebra, a quartic function is a function of the form f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e, where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
In context|mathematics|lang=en terms the difference between quartic and quadratic. is that quartic is (mathematics) an algebraic equation or function of the fourth degree while quadratic is (mathematics) a quadratic polynomial, function or equation.
Coefficients degree
The highest power of the variable that occurs in the polynomial is called the degree of a polynomial. The leading term is the term with the highest power, and its coefficient is called the leading coefficient.
definition of a rational function
The highest power of the variable that occurs in the polynomial is called the degree of a polynomial. The leading term is the term with the highest power, and its coefficient is called the leading coefficient.
definition of an algebraic function
An algebraic function is a function which satisfies , where is a polynomial in and. with integer coefficients. Functions that can be constructed using only a finite number of elementary operations together with the inverses of functions capable of being so constructed are examples of algebraic functions.
