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# Precalculus MATH 3C

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This 2 page Class Notes was uploaded by Claire Harris I on Thursday October 22, 2015. The Class Notes belongs to MATH 3C at University of California - San Diego taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/226778/math-3c-university-of-california-san-diego in Mathematics (M) at University of California - San Diego.

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Date Created: 10/22/15

Math 3C Review Sheet UCSD Winter 2008 1 Functions in general m 53 00l Ways of expressing table graph formula words Input and output domain and range Interval notation Describing change of a function average rate of change increasing and decreasing functions concavity Short run behavior zeros vertical asymptotes holes etc Long run behavior horizontal asymptotes dominance long run similarity of functions Periodic functions period amplitude midline Trigonometric functions as examples See below Piecewise de ned functions Example absolute value function f Operations on functions a Composition fgz b Arithmetic combinations f fgz etc c Inverse function f 1y nd input for a given output i Horizontal line test for invertible functions ii Finding formula by solving y f for z iii Graph re ection about diagonal line y z domain and range swap iv Composition of inverses ff 1z f 1fz x v Examples see below d Transformations of functions i Inside and outside changes horizontal and vertical ii Shifts stretchescompressions re ections ips iii Even and odd functions Math 3C Review Sheet UCSD Winter 2008 2 Speci c families of functions 1 Linear functions a Constant rate of change slope Graph straight line b Formulas for linear functions slope intercept form y mz b point slope form y 7 yo mz 7 zo standard form Ax By O 0 c Solving linear equations and linear systems Parallel and perpendicu lar lines 2 Exponential and logarithmic functions a Properties of exponents and logarithms logab log a 10gb etc b Graphs and general shape Example of inverse functions c Solving equations usinginvolving exponents and logarithms Finding formulas for exponential functions d Applications interest population growth radioactive decay logarith mic scales etc 3 Trigonometric functions sin t cos t tant a De nitions in terms of unit circle Special angles g etc Symmetry properties even and odd functions b Radian measure and arc length c Sinusoidal functions transformations of sint and cos t Effect on pe riod amplitude midline phase shift d Trigonometric identities Pythagorean identity double angle formula phase shifts by 27139 7r e Inverse trigonometric functions arcsint 0r sin 1 t etc Restriction of domain to avoid failure of horizontal line test f Applications i Solving right triangles adjacentoppositehypotenuse ii Solving non right triangles law of sines law of cosines iii Modeling periodic behavior

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