Top 10 of Set 1 Review Domain and Range Inverses Odd and even rules for a function Questions: 2,3,7,10,11,12,13,20,23,31

Generally, the domain is implied to be the set of all real numbers that yield a real number functional value (in the range). Some restrictions to domain: 1. Denominator cannot equal zero (0). 2. Radicand must be greater than or equal to zero (0). 3. Practical problems may limit domain. Domain of a Function

What’s the range of the following a)y=2x+5 b) f(x)=4-x 2 Range of a function

Horizontal line test Horizontal line test. passes inverse is a function If the original function passes the horizontal line test, then its inverse is a function. does not pass inverse is not a function If the original function does not pass the horizontal line test, then its inverse is not a function. Does the Function have an Inverse? Graph does not pass the horizontal line test, therefore the inverse is not a function.

Find an inverse of y = -3x+6. Steps: -switch x & y -solve for y y = -3x+6 x = -3y+6 x-6 = -3y

Meaning find f(g(x)) and g(f(x)). If they both equal x, then they are inverses. Verify that f(x)=-3x+6 and g(x)= -1 / 3 x+2 are inverses Verify the functions are inverses

FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin

1. A function given by y = f(x) is even if, for each x in the domain, f(-x) = f(x). 2. A function given by y = f(x) is odd if, for each x in the domain, f(-x) = - f(x). Even and Odd Functions

Important parts of Trig Graph Determine the amplitude, period, and phase shift of y = 2sin(3x-  ) Solution: Amplitude = |A| = 2 period = 2  /K = 2  /3 phase shift = -C/K =  /3 to the right

Sum and Difference Identities for the Cos Function Trig Identities cos (  +  ) = cos  cos  – sin  sin  cos (  –  ) = cos  cos  + sin  sin  Sum and Difference Identities for the Sin Function sin (  +  ) = sin  cos  + cos  sin  sin (  –  ) = sin  cos  – cos  sin  Sum and Difference Identities for the Tan function tan (  +  ) = tan  + tan  1 - tan  tan  tan (  –  ) = tan  – tan  1 + tan  tan 