Basic functions and transformations/graphing polynomials and rational functions

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Basic functions and transformations/graphing polynomials and rational functions

rational functions

To graph a rational function find the values of y for several different values of x. plot the points and draw the line to connect the points the graph cannot cross the vertical asymtopes.

Polynomials

Graphing a polynomial function will touch the x-axis at zeros with even multiplicities, the graph will cross the x-axis with odd multiplicities and the sum of the multiplicities is the degree of the polynomial function.

y=-f(x)

reflects it across x-axis

y=f(Cx)

C>1 compresses it in x- direction

y=Cf(x)

c>1 streches it in y-direction

0

y=f(x+c)

c>0 moves it left

c<0 moves it right

y=f(x)+c

c>0 moves it up

c<0 moves it down