x and y-intercepts 1.2 2006/04/03 04:43:37 GMT-5 2006/05/01 18:45:30.916 GMT-5 Pradnya Vinay Bhawalkar pradnyab89@gmail.com Kim Dodge Johnston kim.johnston@fortbend.k12.tx.us Pradnya Vinay Bhawalkar pradnyab89@gmail.com intercept rational root solution x intercept y intercept zero Finding x & y intercepts A rational function is a function of the form R x p x q x , where p and q are polynomial functions and q 0 .The domain is all real numbers except for numbers that make the denominator = 0.x-intercepts are the points at which the graph crosses the x-axis. They are also known as roots, zeros, or solutions. To find x-intercepts, let y (or f(x)) = 0 and solve for x. In rational functions, this means that you are multiplying by 0 so to find the x-intercept, just set the numerator (the top of the fraction) equal to 0 and solve for x. Remember: x-intercepts are points that look like (x,0)For y x 1 x 2 find the x-interceptThe x-intercept is (1,0) since x 1 0 , x 1 The y-intercept is the point where the graph crosses the y-axis. If the graph is a function, there is only one y-intercept (and it only has ONE name)To find the y-intercept (this is easier than the x-intercept), let x = 0. Plug in 0 for x in the equation and simplify.Remember: y-intercepts are points that look like (0,y)For y x 1 x 2 find the y-intercept The y-intercept is (0, -1 2 ) since 01 02 -1 2 Find the x- and y-intercepts of the following: y 1 x 2 x-intercept: None since 1 0 y-intercept: (0, 12) since 1 0 2 1 2 y 1 3 x 1 x x-intercept: (13,0) since 1 3 x 0 , -3 x -1 , x 1 3 y-intercept: (0,1) since 1 3 0 1 0 1 y x 2 x 2 9 x-intercept: (0,0) since x 2 0 , x 0 y-intercept: (0,0) since 0 2 0 2 9 0 9 0 or because the x-intercept is (0,0) y x 1 x 2 2 x-intercept: (-1,0) since x 1 0 , x 1 0 , x 1 y-intercept: (0, 14 ) since 0 1 0 2 2 1 2 2 1 4 y 3 x x 2 x 2 x-intercept: (0,0) since 3 x 0 , x 0 y-intercept: (0,0) since the x-intercept is (0,0) y 1 x 3 1 x-intercept: (2,0) since 1 x 3 1 0 , 1 x 3 1 , x 3 1 , x -2 , x 2 y-intercept: (0, 2 3 ) since 1 0 3 1 -1 3 1 2 3 y x 2 4 x 1 x-intercepts: (-2,0), (2,0) since x 2 4 0 , x 2 4 , x -2 , x 2 y-intercept: (0, -4) since 0 2 4 0 1 4 1 -4 y 4 5 x 2 2 x-intercept: None since 4 5 x 2 2 0 , 5 x 2 2 -4 , -4 x 2 8 5 , -4 x 2 13 , x 2 13 4 , a number squared will never be a negative number, so there is no x-intercept y-intercept: (0, 13 2 ) since 4 5 0 2 2 4 5 2 13 2 y 5 x 2 x 3 x-intercept: ( 2 5 , 0) since 5 x 2 0 , 5 x 2 0 , 5 x 2 , x 2 5 y-intercept: None since y 5 0 2 0 3 takes the square root of a negative number. y x 3 8 x 2 1 x-intercept: (2,0) since x 3 8 0 , x 2 x 2 2 x 4 0 , x 2 y-intercept: (0,-8) since 0 3 8 0 2 1 8 1 -8