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ExpoandPower

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Exponents and Power Mathematics at IGCSE and O Level
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   www.mathletics.com Curriculum ReadyExponential and Power Graphs Exponential and Power Graphs  SERIES TOPIC K  1 100% Exponental and Power Graphs Mathletics 100% © 3P Learning Exponential & Power Graphs 11   EXPONENTIAL & POWER GRAPHS Answer these quesons, before  working through the chapter.Answer these quesons, after   working through the chapter. These are graphs which result from equaons that are not linear or quadrac. The exponenal graph has the variable as the exponent. The power graphs raise the variable to any power n . But now I think: What do I know now that I didn’t know before?  I used to think: Which of these equaons is for an exponenal graph and which is for a power graph: 7  y  x =  or  y x 7 =  ? For which value of  x  is 2  x  equal to zero?Is it possible for 5  y x 4 =  to be negave? Why?Which of these equaons is for an exponenal graph and which is for a power graph: 7  y  x =  or  y x 7 =  ? For which value of  x  is 2  x  equal to zero?Is it possible for 5  y x 4 =  to be negave? Why?  SERIES TOPIC K 11 2 100% Exponental and Power Graphs Mathletics 100% © 3P Learning Exponential & Power Graphs Basics ,1 2- ^ h  ,1 2 ^ h , .1 0 5- ^ h  , .1 0 5 ^ h Exponential Graphs Exponenal graphs are of funcons with the variable in the exponent of the form  y a  x =  or  ya 1  x =  ` j  where 1 a 2 . They have this form: This could also be wrien as a  x - Here are some important properes about exponenal graphs: ã They always  cut the  y -axis at ,0 1 ^ h  since 1 a 0 =  for any value of a . ã The exponenal graph never cuts the  x  -axis  since a  x  is never negave or zero if 0 a 2  . ã The greater the value of a  (the base), the steeper  the curve. -2 -1 0 1 2 432 1  x y The  y -intercept of ALL exponenal curves is always ,0 1 ^ h No  x -intercepts Sketch the graphs of 2  y  x  =  and  y 21  x  = ` j  on the same set of axes  x y x y  y 21  x = ` j  y  2  x =  y a  x =  ya 1  x =  ` j , a 1 ^ h  , a 1- ^ h 11

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