Logarithmic Graphs (HSC SSCE Mathematics Advanced): Flashcards

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Logarithmic Graphs
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General form of logarithmic function

y=loga(x)y = \log_a(x)

Vertical asymptote of y=loga(x)y = \log_a(x)

x=0x = 0

x-intercept of any logarithmic function

(1,0)(1, 0)

Domain of y=loga(x)y = \log_a(x)

x>0x > 0

Range of y=loga(x)y = \log_a(x)

All real numbers (yRy \in \mathbb{R})

Effect of larger base on logarithmic graph

Closer to x-axis, more gradual

Logarithmic functions are inverse of...

Exponential functions

Line of reflection for exponential & log inverses

y=xy = x

Point (a,b)(a, b) on exponential maps to... on logarithmic

(b,a)(b, a)

Growth comparison: exponential vs log (when a>1a > 1)

Exponential grows rapidly, logarithmic grows slowly

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