AP Precalc 1.7-1.12

finding vertical asymptotes

zeros on the denominator

HA: numerator less than denominator

HA: y=0

HA: numerator = denominator

HA: y=ratio of the leading coefficients

HA: numerator greater than denominator

NO HA (slant- do synthetic division)

Finding holes

a zero cancels out in BOTH the numerator and denominator, *plug x-value in the equation to get the y value*

Finding x-intercepts

zeros on the numerator

Finding y-intercepts

plug 0 in for x

end behavior limit function

as x goes to ± infinity, f(x) goes to HA

VA limit function

as x goes to VA, f(x) goes to ± infinity

Hole limit function

as x goes to hole x value, f(x) goes to hole y value

finding end behavior on an equation

subtract num from denom, do normal LC/degree evaluation

test an equation for symmetry

make all values negative, same rules as odd/even functions

critical values (for creating sine chart)

VA and X-intercepts

finding a rational function from a graph

everything normal, at the end plug a GIVEN point into the equation and get the finalized equation

finding the y-value of a hole

plug x-value in the equation to get the y value

how to build pascal’s triangle

start with 1 at top, 1 1 next row, 1 on either sides after that and add the different numbers. row 0 (a+b)^0 is at the top.

horizontal translation left

f(x+h)

horizontal translation right

f(x-h)

vertical dilation

af(x)

horizontal dilation

f(bx) (factor of 1/b units)

negative outside of the parentheses

reflection over the x-axis

negative inside of the parentheses

reflection over the y-axis

transformations that affect the y-values

occur outside the parenthesis

transformations that affect the x-values 

occur inside the parenthesis