Algebraic Functions Theses are functions that are con- structed my adding, subtracting, multiplying or taking roots of polynomials. Ex. 1. Find the domain of f ( x ) = √ x . Draw the graph. 1
2 Ex. 2. Find the domain of f ( x ) = √ x 2 + 1 . Draw the graph.
3 Ex. 3. Find the domain of f ( x ) = √ x 2 - 1 . Draw the graph.
4 Ex. 4. Find the domain of f ( x ) = 4 √ ( x - 3)( x +2) x - 1 .
6 Trigonometric Function Trigonometry means the study of angles inside a triangles. There are two (equivalent) ways of thinking abut trigono- metric functions. By looking at angles inside a triangle, or by looking at a unit circle. Two ways of measuring angles: radian vs degree Unit Circle
7 f ( t ) = sin( t ) f ( t ) = cos( t )
8 For any periodic function: • the Amplitude is half the distance between the max- imum and minimum values. • Period is th smallest time needed for the function to execute one complete cycle. To describe an arbitrary amplitude and period of a sinu- soidal functions, we use functions of the form f ( t ) = A sin( Bt ) g ( t ) = A cos( Bt ) where | A | is the amplitude and 2 π/ | B | is the period.