Chapter 3.5 concepts

Roots x-intercepts (#, 0) roots cannot

1st part of RATEY _______________ Solution to TOP These are ________________ Set ______________ = 0 and solve Write answer as points ___________ *graphs must pass through any __________ on the graph and __________ cross the x-axis

asymptotes vertical denominator x=# close never

2nd part of RATEY ____________ ______________ Solution to the bottom Set ____________________ = 0 and solve. Write answers as lines: _________________ *This acts as a boundary line. the graph comes ___________ but can ______________ cross

tangent together tangent together

3rd part of RATEY (_____________)/(______________) "Special" Squared Terms Special behaviors of the graph _______________- "Special squared" term on TOP: means the graph bounces at that x-intercept ________________"Special Squared" Term On BOTTOM: Means graph will come together at that asymptote

alone yes no

3rd part of RATEY cont... An x^2 term _______________ (monomial) or a factor squared, like (x+5)^2 Examples: ___________ x^2 -2x^2 (x-5)^2 ___________ x^2+2x -x^2+3 2x^2+x-5

ends y=# none y=0

4th part of RATEY This tells how the graph looks on the ____________ to the left and right. 1. Balanced: numerator = denominator _________________ 2. Numerator > denominator _____________ or 3. Numerator < denominator ________________

y-intercept

5th part of RATEY ________________ Set f(x) = 0 to solve

asymptote

A vertical line that the graph of a function approaches, but does not touch, is said to be a vertical _____________________ of the graph.

polynomial

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are ____________________ functions and q(x) does not equal 0

False

T/F The domain of every function is the set of all real number

True

T/F The graph of the reciprocal function f(x)=1/x has a break and is composed of two distinct branches

one more than

The graph of a rational function has a slant asymptote if the degree of the numerator is _________________________________ the degree of the denominator

left right

compared to the graph of f(x)=1/x, the graph of g(x)=(1/(x+6))-3 is shifted 6 units _______________ and 3 units ______________

horizontal asymptote y=0

if the graph of a function f approaches b as x increases or decreases without bounds, the the line of y=b is a ___________________ ____________________ of f. The equation of such a line for the graph of y=(x-10)/(3x^2 + x + 1) is ___________________