HPC Vocab

Solutions of the equation f(x) = g(x) are

the values of x where the graphs of f and g intersect

Vertical line test

a curve in the coordinate plane is the graph of a function if and only if no vertical line intercsects the curve more than once

Local minimum value

if f(a) <= f(x) when x is near a

Local maximum value

if f(a) >= f(x) when x is near a

Average rate of change

change in y/ change in x; f(b)-f(a)/b-a

Net change

change in y; f(b)-f(a)

Transformations

Vertical shifts, horizontal shifts, reflecting graphs, Vertical stretch and shrink of graphs, horizontal stretch and shrink of graphs

Vertical shifts

ex: f(x)= x + 2

Horizontal shifts

ex: f(x)= (x-2), f(x)= (x+2)

Reflecting graphs

y= -f(x), reflect the graph of y= f(x) over the x-axis

y= f(-x), reflect the graph of y= f(x) over the y-axis

Vertical stretch and shrink of graphs

y= cf(x)

Horizontal stretch and shrink of graphs

y= f(cx); if c > 1, shrink by a factor of 1/c, if c < 1 stretch by a factor of 1/c

Even Functions

f is even if f(-x) = f(x) for all x in the domain of f

Odd functions

f is even if f(-x) = -f(x) for all x in the domain of f

One to one function

no two elements in the domainof f correspond to the same element in the range of f

Horizontal line test

every horizontal line intersects the graph of the function at most once

Definition of an inverse function

f^-1(y) = x == f(x)=y

Inverse function property

f^-1(f(x)) = x for every x in A

f(f^-1(x)) = x for every x in B