Pg. 235/244 Homework Study for the Quiz!! #3(-∞, 0)U(0, ∞) #5(-∞, -1)U(-1, 1)U(1, ∞) #7(-∞, -1)U(-1, 3/2)U(3/2, ∞) #9g(x) = 1/x#11g(x) = 3#13g(x) = x x = 3; y = 0; EB model is g(x) = 2/x # oz of 100% barium #3#5x = 1 #7x = 0, -1, 1#9

4.1/4.2 Rational Functions, Asymptotes and Graphs Basic Information Domain is determined by the existence of the denominator. Horizontal Asymptotes tell you the potential end behavior of a function. They can be crossed “in the middle.” Vertical Asymptotes occur when the function heads to ±∞ from either side of a value. They can not be crossed. Vertical Asymptotes are found when the denominator is set equal to zero and solved. Horizontal Asymptotes are determined by the degrees in the numerator and denominator. – Top Heavy means there is no Horizontal Asymptote, but there is a Diagonal Asymptote of sorts. – Bottom Heavy means the Horizontal Asymptote is y = 0 – Equal Degrees means the Horizontal Asymptote is where a and b are coefficients of the degree terms in the numerator and denominator

4.1/4.2 Rational Functions, Asymptotes and Graphs Hidden Asymptotes Sometimes there will be an asymptote that is not perfectly horizontal or vertical. This occurs when the degrees are “Top Heavy” To find the “hidden” asymptote when the functions are “Top Heavy” you must divide the functions out. Examples Graph the following rational function using the given steps provided before.

4.2 Rational Functions and Graphs Rational Functions Review How do you find intercepts? Tell me about: – Vertical Asymptotes – End Behavior Models – Horizontal Asymptotes (2) – Top Heavy cases – When there are holes in a graph – When a graph increases/decreases – Domain and Range Word Problems! Pure acid is added to 150 ounces of a 50% acid solution to produce a new mixture that is 78% acid. How much acid was added?