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Level 540

Exponential & Logarithmic Functions


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Exponential Function:
The inverse of an Logarithmic function
Logarithmic function:
The inverse of an exponential function
Asymptote:
a straight line that is the limiting value of a curve a line which a graph never crosses
base:
the number that serves as a starting point for a logarithmic or other numerical system
common logarithm:
a logarithm to the base 10
inverse function:
the function obtained by expressing the dependent variable of one function as the independent variable of another
natural logarithm:
a logarithm to the base e
exponential growth:
growth of a population that multiplies by a constant factor at constant time intervals
exponential decay:
a decrease that follows an exponential function
natural base:
exponetial function with base e
principal:
the original amount on which interest is calculated
compound interest:
Interest calculated on both the principal and the accrued interest.
rational exponent:
an exponent that can be expressed as m/n , where m and n are integers and n ≠ 0
(0,1) and (1,b)
Points on parent graph (exponential form)
(1,0) and (b,1)
Points on parent graph (logarithmic form)
Asymptote (exponential form)
Parent graph: Y=0
Asymptote (logarithmic form)
Parent graph: X=0
Domain (exponential form)
All real numbers
Domain (logarithmic form)
When a>0: values > Asymptote
Range (exponential form)
When a>0: values > Asymptote
Range (logarithmic form)
All real numbers
Reflections (exponential form)
when a<0, reflection over X-axis
Reflections (logarithmic form)
when a<0, reflection over X-axis
horizontal?
Vertical stretch: a ≠ 0
Stretches (logarithmic form)
Vertical stretch: a ≠ 0