4.4 Graph Exponential 4.4 Graph Exponential Growth FunctionsGrowth Functions

VocabularyVocabulary

Exponential FunctionExponential Function: : y = aby = abxx, where , where aa ≠ 0 and the base ≠ 0 and the base bb is a positive number is a positive number other than 1.other than 1.Examples:Examples:

Exponential Growth & DecayExponential Growth & Decay

y = aby = abxx

VocabularyVocabulary

asymptoteasymptote: : line that the graph line that the graph approaches more and more closely, but approaches more and more closely, but does not touch or crossdoes not touch or cross

VocabularyVocabulary

end behaviorend behavior of a function’s graph: the of a function’s graph: the y-behavior of the graph as x approaches y-behavior of the graph as x approaches positive or negative infinity.positive or negative infinity.

Graphing y = bGraphing y = bxx

Graph y = 4Graph y = 4xx

X Y X Y -2-2 -1-1 00 11 22

Graphing y = abGraphing y = abxx

GraphGraph

X Y X Y -1-1 00 11

2 3xy

Graphing y = abGraphing y = abxx

GraphGraph

X Y X Y 00 11 22

13

3xy

Graphing y = abGraphing y = abx-hx-h+k+k

22 3 1xy

Translates the graph

left 2 unitsTranslates the graph

down 1 unit

Graphing y = abGraphing y = abx-hx-h+k+k

GraphGraph

22 3 1xy

ClassworkClasswork

p. 121 #’s 1-3p. 121 #’s 1-3 (graph the functions) (graph the functions)

p. 122 #’s 4-6p. 122 #’s 4-6 (graph the functions) (graph the functions)

HomeworkHomework

Pg. 122, 1 – 17 allPg. 122, 1 – 17 all