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Level 392

Graphing Rational Expressions


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Ignore?
No, only want reals.
Does a graph have to have an X intercept?
To find an x intercept
Set the numerator equal to 0 and solve for x
No, but most it can have is 1.
Does a graph have to have a Y intercept?
To find a y intercept
Substitute 0 for x in denominator and solve
Domain
The ______________________ is all the possible INPUT, X, values.
Substitute x coordinate into simplified expression
To find the y coordinate of a hole
Horizontal Asymptotes
y=0 when degree of denominator > degree of numerator
Vertical Asymptotes
zeroes of denominator
To find vertical asymptotes
Set denominator equal to zero solve for x
No, but can have more than 1
Does a graph have to have a vertical asymptote?
Horizontal Asymptotes occur when
Degree of the numerator is less than the degree of the denominator
The horizontal asymptote is y=0
When the degree of the numerator is less than the degree of the denominator
The horizontal asymptote is y= ratio of leading coefficients
When the degrees of the numerator and denominator are the same
y→HA
When there is a horizontal asymptote the EB is
Slant asymptotes occur when
Degree of the numerator is one more than the degree of the denominator
Synthetic division
To find a slant asymptote
L:y→-∞ R:y→∞
When the slope is positive
L:→∞ R:y→-∞
When the slope is negative
Factor the numerator and denominator.
Step 1 of graphing rational expressions
y=0
If degreevof numerator is less than degree if denominator...
Y=ratio of lead coefficient
If degree of numerator is = degree of denominator. ..
There is no HA but SA is present.
If degree of numerator is greater than degree of denominator. ..
Holes
when same factor occurs in numerator and denominator
X intercepts
Ordered pair
Y intercepts
Ordered pair
Min/max
Ordered pairs
Range
The difference between the greatest number and the least number in a set of data.