Determining Rules for Graphs of Exponential and Logarithmic Functions (VCE SSCE Mathematical Methods): Flashcards

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Determining Rules for Graphs of Exponential and Logarithmic Functions
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Points needed for 2 unknown parameters

2 points on the graph

aa in y=aex+by = ae^x + b controls

Vertical stretch/compression

bb in y=aex+by = ae^x + b represents

Vertical shift

Horizontal asymptote of y=aex+by = ae^x + b

y=by = b

bb in y=aloge(x+b)y = a\log_e(x + b) represents

Horizontal shift

Vertical asymptote of y=aloge(x+b)y = a\log_e(x + b)

x=bx = -b

Use of form y=Aebty = Ae^{bt}

Modelling growth and decay

Asymptote suggesting y=aex+by = ae^x + b

Horizontal asymptote

Asymptote suggesting logarithmic function

Vertical asymptote

Value of loge1\log_e 1

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