Types of functions

Types of functions

1. Polynomial

   • Linear
     • Y=mx+b
       • -m and b are constants. m is the slope and b is the Y intercept.
         • Y=mx+b
           • If m is positive the line rises to the right and if m is negative then the line falls to the right
   • Quadratic
     • Y=ax^2+bx+c
       • a, b and c are constants
         • Their graphics are called parabolas. If a is negative number then the parabola opens downward and if a is positive number then the parabola opens upward
           • • Applications: They're used to describe real phenomena like:concentration of a substance in a compound, distance traveled by a mobile at constantspeed, buying items unit price, etc.
   • Polynomial
     • Y=anx^n+an-1x^n-1+...+a2x^2+a1x+a0
       • an,an+1,a2 and a1 are constants
         • The highest power of x that ocurrs is called the degree of the polynomial. Only whole number powers of x are allowed
           • • Applications: They have many applications in numerical analysis to approximate results of other harder functions

2. Special

   • Rational
     • y= p(x)/q(x)
       • When the polynomial in the denominator is 0 then the rational function becomes infinite as indicated by a vertical dotted line called an asymptote
   • Radicals
     • Y= /x
       • The independent variable is inside the root
         • • Applications: The side of a ground i function of his area

3. Transcendental

   • Logarithmic
     • Y=aln(x)+b
       • x is in the natural logarithm and a and b are the constants
         • They are only defined for positive x, for small x they are negative and for large x they are positive but stay small
           • • Applications: Geology as a science requires the approach of logarithmic equations to calculate the intensity of an event. The astronomers to determine a stellar magnitude of a star or lanet
   • Exponential
     • Y=b^x
       • x is in an exponent and b is a constant
         • If the base b is greater than 1 then the result is exponential growth and if the base b is smaller than 1 then the result is exponential decay
           • • Applications: It's used to calculate the growth of a variable
   • Trigonometrics
     • Y=sin(x+a)
       • Sine, cosine, tangent, etc. Used in geometry and to describe periodic phenomena
         • • Applications: They're used to calculate distances without the need to travel and setle through triangles, circumference and others. Engineers use them to measure heights or distance, angle, measurement perform, etc.

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