Functions of
One Independent Variable/Range/Domain/Even/Odd
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In a Nut Shell: Calculus involves
different types of functions, how to evaluate them, how to express them in
different ways, how to evaluate changes in them, how to graph them, etc. A function of one
independent variable, x, typically is written as f(x). i.e. y =
f(x) - reads as
y is a function of x x is
the independent variable f(x) is the dependent variable i.e.
for each x, y takes on the value f(x) |
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Definition: The set of values of x
where f(x) is defined is called
its domain Definition: The set of values of f(x) where it is defined is called the range of
f |
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Domains can be Open, half
open, and closed intervals ( ---------------------- ) i.e.
˗ 3 < x
< 9 example of open interval [ ---------------------- )
i.e. ˗ 3 ≤
x < 9 example of half open interval ( ---------------------- ]
i.e. ˗ 3 < x
≤ 9 example of half
open interval [ ---------------------- ] i.e.
˗ 3 ≤ x ≤
9 example of closed
interval |
|
Graphs of equations and functions – one can graph the straight line
function, y(x): y
= m x +
b m =
slope of line, b =
y-intercept, the value of y when x = 0 slope
= rise over run such as Δy / Δx Slope intercept expression for a
straight line: y =
m x + b Point-Slope form for a straight
line: y ˗
yo =
m ( x - xo ) where (xo, yo) is any point on the line |
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In a Nutshell: A function, f(x), is said
to be even if f(x)
= f( ˗ x ) and odd
if f(x) = ˗ f( ˗x ). A simple example of an
even function is f(x) = x2 and one of an odd function is f(x)
= x . |
| Return to Notes for Calculus 1 |
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