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Key Terms

A line which a graph of a function approaches closely but never touches.
common logarithmic function
The function f(x)=logxf(x)=logx is the common logarithmic function with base10,10, where x>0.x>0.
y=logxis equivalent tox=10yy=logxis equivalent tox=10y
exponential function
An exponential function, where a>0a>0 and a1,a1, is a function of the form f(x)=ax.f(x)=ax.
logarithmic function
The function f(x)=logaxf(x)=logax is the logarithmic function with base a,a, where a>0,a>0,x>0,x>0, and a1.a1.
y=logaxis equivalent tox=ayy=logaxis equivalent tox=ay
natural base
The number e is defined as the value of (1+1n)n,(1+1n)n, as n gets larger and larger. We say, as n increases without bound, e2.718281827...e2.718281827...
natural exponential function
The natural exponential function is an exponential function whose base is e: f(x)=ex.f(x)=ex. The domain is (,)(,) and the range is (0,).(0,).
natural logarithmic function
The function f(x)=lnxf(x)=lnx is the natural logarithmic function with base e,e, where x>0.x>0.
y=lnxis equivalent tox=eyy=lnxis equivalent tox=ey
one-to-one function
A function is one-to-one if each value in the range has exactly one element in the domain. For each ordered pair in the function, each y-value is matched with only one x-value.
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