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 a, b 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 xb,
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 · xn + an −1 · xn −1 + … + a2 · x 2 + a1 · x + a0,
where an, an −1, … , a2, a1, a0 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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