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how to find vertical asymptotes
factor the denominator... value(s) of x that make denominator = 0 represent vertical asymptotes of the graph
Horizontal Asymptotes occur when
Degree of the numerator is less than the degree of the denominator
oblique asymptotes occur when...
(degree of numerator) = (degree of denominator) + 1
removable discontinuities occur when...
there is a common term in the numerator and denominator that can be canceled
the equation: y = the ratio of the leading coefficients of P(x) and Q(x)
if the degrees are equal, then the horizontal asymptote of the graph is represented by...
the equation: y = 0
if the degree of the numerator is smaller than that of the denominator, then the horizontal asymptote of the graph is represented by...
y = the quotient when P(x) is divided by Q(x)
the equation that represents the slant asymptote of the graph is the line...
the x coordinate of a hole is...
the value of x that would make the canceled term equal to zero
the y coordinate of the hole is...
the value obtained by substituting the given value of x into the reduced form of the rational function
NO!
if there is a removable discontinuity in a polynomial, does that value represent a vertical asymptote?
techniques for evaluating limits of functions
- graph the function by plugging in values
the 2 sided limit does not exist
if 2 sides of a limit approach different y values, then
the horizontal asymptote
finding the limit of f(x) as x approaches infinity is the equivalent of finding
(1.50x+4500)/x, limit A(x) = 1.50
the formula for the average cost C of a product, where x is the number of units, with each product costing 1.50 and with an up front cost of 4500 and its limit
how to simplify (n+1)!/(n-1)!; does its limit exist
(n+1)! = (n+1)+n+(n-1)!, so cancel (n-1)! to get n(n+1); no