135test1Review - MAT135 Test 1 Review 1 1 FUNCTION Function...

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MAT135 Test 1 Review 1 FUNCTION 1 Function Functions are usually represented using a graph or a formula. Function represented by graph/curve 1. The domain is the values of x that the curve is above (or below). 2. Verticle Line test : There should not exist a verticle line that intersect the curve at 2 points. 3. Even Function is when the graph do not change when reflected against the y-axis. 4. Odd Function is when the graph do not change when rotated 180 degrees. 5. Increasing Function is when the graph points to the top-right. 6. Decreasing Function is when the graph points to the bottom-right. Function represented by formula Given a formula f ( x ) 1. The domain is all the possible values of x that f ( x ) makes sense. The range is all the possible values of y = f ( x ). 2. Set y = f ( x ), the function can be plotted to create a graph, with y being the height. 3. Piecewise Function is when f ( x ) is given by one expression for some values of x , and another expression for some other values of x . 4. Even Function is when f ( - x ) = f ( x ). Replacing every x with - x in the formula do not change it. 5. Odd Function is when f ( - x ) = - f ( x ). Replacing every x with - x in the formula causes it to gain a minus sign on the outside. 6. Increasing Function : When x 1 < x 2 , f ( x 1 ) < f ( x 2 ). 7. Decreasing Function : When x 1 < x 2 , f ( x 1 ) > f ( x 2 ). Author: Xiao (TA) Page 1
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MAT135 Test 1 Review 1 FUNCTION Various Special Functions 1. Absolute Value Function , f ( x ) = | x | is given piecewise: f ( x ) = x if x 0, and f ( x ) = - x if x < 0. The absolute value around a number makes the number positive. 2. Polynomial Function are different powers of x added together. f ( x ) = 5 x 3 + 2 x 2 + x + 3 is an example. The powers of x can be as high as you like, and the numbers in front of x can be anything you like. 3. Rational Function is the division of 2 polynomials. Example: f ( x ) = 2 x 2 + 3 3 x 3 Notice that the denominator can not be 0, so there are values of x that can’t be used. 4. Square Root Function is given by f ( x ) = x . We require that x must be positive for this function. 5. Trignometric Functions : f ( x ) = sin ( x ) has a period of 2 π .
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