Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewIn this one you’ve got to be a little careful. First factor the numerator anddenominator.2x −5x− 6 ( x− 6)( x+1)2 =6x−x x 6−x( )At first glance it doesn’t look like anything will cancel. However remember thata− b=− b−a( )Using this on the term in the denominator gives the following.2x −5x− 6 ( x− 6)( x+ 1)( x− 6)( x+1)x+ 1 x+1= = = = −26x−x x 6−x −x x−6−x x( )Also recall thata −a a= = −−b b bso it doesn’t matter where you put the minus sign.( )Graphing and Common GraphsSketch the graph of each of the following.1.2y =− x+35SolutionThis is a line in the slope intercept formy = mx + bIn this case the line has a y intercept of (0,b) and a slope of m. Recall that slope canbe thought of asrisem =runIf the slope is negative we tend to think of the rise as a fall.The slope allows us to get a second point on the line. Once we have any point on theline and the slope we move right by run and up/down by rise depending on the sign.This will be a second point on the line.2In this case we know (0,3) is a point on the line and the slope is − . So starting at5(0,3) we’ll move 5 to the right (i.e. 0→ 5) and down 2 (i.e. 3→ 1) to get (5,1) as asecond point on the line. Once we’ve got two points on a line all we need to do isplot the two points and connect them with a line.Here’s the sketch for this line.© 2006 Paul Dawkins 20http://tutorial.math.lamar.edu/terms.aspx