Name some functions, the different forms of equations of lines and how to graph them Thank You!?

Mathematics
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Math , please help

Apr 28th, 2015

1) Linear equations=

These are functions of the form:

y = m x + b,
where m and b are constants. A typical use for linear functions is converting from one quantity or set of units to another. Graphs of these functions are straight. m is the slope and b is the y-intercept. If m is positive then the line rises to the right and if m is negative then the line falls to the right. 

 

2) Quadratic functions;these are functions of the form:
y = a x2+ b x + c,
where ab and c are constants. Their graphs are called parabolas. This is the next simplest type of function after the linear function. Falling objects move along parabolic paths. If a is a positive number then the parabola opens upward and if a is a negative number then the parabola opens downward.

3)  Power functions;These are functions of the form:
y = a x b,
where a and b are constants. They get their name from the fact that the variable x is raised to some power. Many physical laws (e.g. the gravitational force as a function of distance between two objects, or the bending of a beam as a function of the load on it) are in the form of power functions. We will assume that a = 1 and look at several cases for b:

 See the graph to the right. When x = 0 these functions are all zero. When x is big and positive they are all big and positive. When x is big and negative then the ones with even powers are big and positive while the ones with odd powers are big and negative. 






4) Polynomial functions;These are functions of the form:

y = an · x n + an −1 · x n −1 +  …  + a2 · x 2 + a1 · x + a0,
where anan −1,  … , a2a1a0 are constants. Only whole number powers of x are allowed. The highest power of x that occurs is called the degree of the polynomial. The graph shows examples of degree 4 and degree 5 polynomials. The degree gives the maximum number of “ups and downs” that the polynomial can have and also the maximum number of crossings of the x axis that it can have.


Apr 28th, 2015

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