Study Flashcards
A rational function has the form
f(x) = N(x)/D(x) where N(x) and D(x) are polynomials
f(x) = N(x)/D(x) where N(x) and D(x) are polynomials
Rational number form
A number is NOT a polynomial when
Negative exponents, variable in denominator, or radicals
Negative exponents, variable in denominator, or radicals
Factors that make a number NOT a polynomial
How is the domain of a number with 4 and 2 as its zeros written?
(-∞, 2)U(2,4)U(4, ∞) because 3 is still included
When a line has an excluded number from the domain, what happens to the graph?
A hole in the line
A hole in a line on a graph appears when
A function has an excluded number from the domain at a certain x
How is f(x)=1/x drawn on graph?
Day 16 page 3
If x > 0, as x gets smaller (close to 0), 1/x gets larger without bound. How is this represented?
Lim x — > 0 +
Lim x — > 0 +
As x approaches 0, the function gets bigger with bound
If x < 0, as x gets closer to 0, 1/x gets smaller without bound. How is this represented?
Lim x — > 0 -
Lim x — > 0 -
As x approaches 0, the function gets smaller with bound
The line x = a is a vertical asymptote of f if
Lim f(x) = +- ∞ x — > a
Lim f(x) = +- ∞ x — > a
The line x = a is a vertical asymptote of f
As x gets larger (x > 0), or farther from 0, 1/x gets smaller approaching 0. How is this represented?
Lim 1/x = 0
x — > ∞ and x — > -∞
Lim 1/x = 0
x — > ∞ and x — > -∞
As x gets larger (x > 0), or farther from 0, 1/x gets smaller approaching 0.
The line y=k is a horizontal asymptote of f if
Lim f(x) = k x — > +- ∞
Lim f(x) = k x — > +- ∞
The line y=k is a horizontal asymptote of f
The function g(x) = ax + b/ cx +d is a transformation of
f(x) = 1/x