5 with two vertical asymptotes find at least 4 key points to graph in addition to x and y intercepts ex 2 graph d vertical asymptotes y int x int 30 problems find the vertical asymptotes horizontal problems find the vertical asymptotes horizontal asymptotes slant asymptotes and holes and intercepts for find the equations of both vertical and horizontal asymptotes horizontal asymptote equation jennarocca domain vertical asymptotes and horizontal asymptotes overview find the equations of both vertical and horizontal asymptotes calculus review of horizontal asymptotes 3 a rational function is the ient of two polynomial functions the domain of a rational function is all real numbers excluding numbers that make most viewed thumbnail vertical and horizontal asymptotes 13 example 2 finding vertical and horizontal asymptotes find all vertical and horizontal asymptotes of essential question how do you find intercepts vertical asymptotes horizontal asymptotes and holes 15 15 4 ex 1 graph d y int x int holes if anything cancels then there is a hole none vertical asymptote horizontal asymptote other key points 1 objective tsw determine vertical horizontal and oblique 10 finding vertical asymptotes this graph follows a horizontal line red in the diagram as it moves out of the system to the left or right this is a horizontal asymptote with the 4 finding vertical asymptotes rules for graphing rationals eba find the domain of the function and the vertical and horizontal asymptotes find the equation for each horizontal asymptote 10 finding vertical asymptotes 19 find the asymptotes of each finding horizontal asymptotes example 4 3 finding horizontal asymptotes 41 we can find the coordinates of the hole by finding an equivalent rational function to f x that has all the same points of f x except at the point at x 2 example 2 finding vertical and horizontal asymptotes find the horizontal asymptote 3 find the equations of the horizontal asymptotes of rules for graphing rational functions vertical asymptotes essential question how do you find intercepts vertical asymptotes horizontal asymptotes and holes 5 domain vertical asymptotes horizontal asymptotes holes intercepts essential question how do you find intercepts vertical asymptotes horizontal asymptotes and holes graph with vertical asymptote x 1 horizontal asymptote y 1 hole at 1 rational functions learning objective to find vertical asymptotes horizontal asymptotes holes and one or two key points then graph rational functions 3 7 notes example 2 find the discontinuities of solution 6 copyright graph of f x x 2 x 3 finding vertical horizontal asymptotes we will use a given rational function as an example to show ytically how to find a vertical asymptote and a hole in the graph of that function ex find a rational function given the vertical asymptotes and intercepts for each equation write the vertical asymptotes of rational functions quick way to find them another example 1 you limits at infinity and horizontal asymptotes graph of f x 4x 2 x essential question how do you find intercepts vertical asymptotes horizontal asymptotes and holes