Intermediate Algebra 2e

# Key Terms

asymptote
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 base$10,10,$ where $x>0.x>0.$
$y=logxis equivalent tox=10yy=logxis equivalent tox=10y$
exponential function
An exponential function, where $a>0a>0$ and $a≠1,a≠1,$ 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 $a≠1.a≠1.$
$y=logaxis equivalent tox=ayy=logaxis equivalent tox=ay$
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, $e≈2.718281827...e≈2.718281827...$
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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