University:
Missouri State University
Course:
MTH 138 | Pre-Calculus Mathematics
Academic year:

2020
Views:

61

Pages:

4
Author:

Rachel Pace

Pre-Calculus/Trig 3 UNIT 1: Algebra II Review - SECTION 7 WORKSHEET #1 To Identify Types of Discontinuity: Step 1: Step 2: Step 3: Step 4: SLANT ASYMPTOTES (Exists only if Horizontal Asymptote is not present) (USE SIMPLIFIED EQUATION) GRAPHING RATIONAL FUNCTIONS HOLES (Removable Discontinuities) Factor numerator & denominator Simplify Name: KEY Date: If anything cancels, then there is a hole (More than one factor cancels → More than one hole) Find the ordered pair, (x, y), substitute x into the SIMPLIFIED EQUATION to get y VERTICAL ASYMPTOTES (USE SIMPLIFIED EQUATION) Set simplified equation denominator = O_{x} solve for x HORIZONTAL ASYMPTOTES-Two Cases (USE SIMPLIFIED EQUATION) Degree of Denominator Degree of Numerator y = 1 ratio of leading coefficients Degree of Denominator > Degree of Numerator y = 0 Degree of Numerator is ONE degree larger than the Degree of Denominator Use Long Division ignore the remainder Answer in the form y = mx + b Directions: State each discontinuity, x-intercept, and y-intercept. Then sketch a graph. 1.) f(x) = (x ^ 2 - 4)/(x - 2) x + 2 10 8 HOLE y = 4 y = (x) - 2 KINT x = - 4 0 = x - 2 10 10 -2- -10 HOLE(S) VERTICAL ASYMPTOTE(S) HORIZONTAL ASYMPTOTE SLANT ASYMPTOTE x-intercept(s) y-intercept (2,4) NONE ENTIRE DENUMINATIC CANCELED NE KYMPOTES! NONE NONE (-2,0) (0, alpha) y =o+ perp y - 2 x = 2 x - lambda = 0 ((x + 2)(x - 2))/(x - 2) 2.) f(x) = - 2/((x - 3) ^ 2) VA X-300 13 Y -2 (Q - 1) ^ + = -2 (*3)^ 2 4/9 10 2+ -10 10 -10 HOLE(S) NONE VERTICAL ASYMPTOTE(S) X - 3 HORIZONTAL ASYMPTOTE y + 0 SLANT ASYMPTOTE NOVE x-intercept(s) NONE y-intercept (0, - 2/9) -5 10 10 3.) f(x) = - 5/(x ^ 2 - 2x - 3) - 5/((sqrt(- 5))(x + 1)) VA X-3-0 43 x + f = 0 x - 1 - 5/((0a)(phi + 1)) (- T)/((- 1)(i)) - 5/- 3 / (5/3) -10 HOLE(S) NONE VERTICAL ASYMPTOTE(S) x + 1 X3 HORIZONTAL ASYMPTOTE y = 0 SLANT ASYMPTOTE NONE x-intercept(s) NONE y-intercept (0, 5/3) 4.) f(x) = (x ^ 3 + 4x ^ 2 - 21x)/(x ^ 2 + 4x - 21) = (x(x ^ 2 + 1 / y - 3))/((x + 7)(x - 3)) X (x(x + 7)(x - 7))/((x + 7)(x - 3)) HOLES 70 x = - 7 x - 3 X > S y(- 7) Y = - 7 (3) y = 3 → -10 10 -2+ -10- 0 - x YINT y - 2 HOLE(S) (-7,-71 (3,3) VERTICAL ASYMPTOTE(S) NONE HORIZONTAL ASYMPTOTE NONE 10 SLANT ASYMPTOTE NONE x-intercept(s) (0,0) 10 y-intercept (0,0) 5.) f(x) = (x ^ 2 + 5x + 8)/(x + 3) VA x +3 sim x Y - 3 158 1-76 y = x + 2 -10 10 2+ INT: Y= (0) ^ 2 + 5(6) + 8 (0+3 8/3 HOLE(S) NONE VERTICAL ASYMPTOTE(S) x = - 3 HORIZONTAL ASYMPTOTE NONE SLANT ASYMPTOTE y = x + 2 -10 x-intercept(s) NONE y-intercept (0)

Pre-Calculus Section 1.7 Worksheet 1 Key

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