Graphing Rational Functions SHRATEY Graphing Rational Functions Using

Graphing Rational Functions SHRATEY

Graphing Rational Functions Using “SHRATEY” In Pre-Cal we add two other steps to the beginning of RATEY to identify any holes in our graph, this turns RATEY into SHRATEY: S - Simplify H – Holes R – Roots A – Asymptotes T – Tangent/Together E – End Behavior Y – Y-Intercept

SIMPLIFY – Simplify the equation Factor the numerator (if possible) Factor the denominator (if possible) Cancel any factors that occur in the numerator AND the denominator.

HOLES – Locate any holes created by factors that cancel If any factors canceled above, they create holes in the graph. Set the factor = 0 and solve for x. Plug the x-value into the simplified equation to fin the y-value of the hole. Write answers as points: (x, y)

THE REST OF THE STEPS ARE THE SAME!!

RATEY Examples Day 3 - #1

RATEY Examples Day 3 - #1 Already in simplest terms No factors cancel, this means no holes Since top doesn’t factor, there are NO ROOTS X+2=0 x = -2 There is a vertical asymptote at x = -2 x -4 x 2 -2 x +2 -x 2 -2 x ↓ 0 -4 x +2 4 x 8 Neither x +2 Top heavy means oblique asymptote – use synthetic or long division to find the asymptote. We ignore the remainder and use only the quotient. The end behavior follows the line y = x-4 Y=(02 – 2(0) + 2)/(0+2) = 2/2 = 1 y-intercept is (0, 1) 10

RATEY Examples Day 3 - #2

RATEY Examples Day 3 - #2 Already in simplest terms No factors cancel, this means no holes Since top doesn’t factor, there are NO ROOTS X-3=0 x=3 There is a vertical asymptote at x = 3 Neither Top heavy means oblique asymptote The end behavior follows the line y = 2 x+7 Y=(2(0)2 + 0 + 1)/(0 -3) = 1/-3 = -1/3 ≈ -0. 33 y-intercept is (0, -0. 33) x -3 2 x +7 2 x 2 +x +1 -2 x 2 +6 x ↓ 0 7 x 1 -7 x +21 0 22

ASSIGNMENT RATEY Worksheet #3