University:
Glendale Community College
Course:
MAT150 | College Algebra/Functions
Academic year:

2021
Views:

397

Pages:

14
Author:

emaiftAddiniaf5

Section 5.4: Properties of rational functions 1) 𝑓(𝑥) = 2𝑥−6 𝑥+2 Use the graph of 𝑓(𝑥) the function to find the following, then confirm your answer using Algebra. a) find the domain, express your answer using interval notation (−∞, −2) ∪ (−2, ∞) b) find the equation of the vertical asymptote(s) 𝑥 = −2 c) find the equation of the horizontal asymptote 𝑦 = 2 d) find the x- intercept (3,0) e) find the y-intercept (0, −3) 4𝑥−12 3) 𝑓(𝑥) = 2𝑥+12 Use the graph of 𝑓(𝑥) the function to find the following, then confirm your answer using Algebra. a) find the domain, express your answer using interval notation (−∞, −6) ∪ (−6, ∞) b) find the equation of the vertical asymptote(s) 𝑥 = −6 c) find the equation of the horizontal asymptote 𝑦 = 2 d) find the x- intercept (3,0) e) find the y-intercept (0. −1) 𝑥−14 5) 𝑓(𝑥) = 𝑥 2 +6𝑥−7 Use the graph of 𝑓(𝑥) the function to find the following, then confirm your answer using Algebra. a) find the domain, express your answer using interval notation (−∞, −7) ∪ (−7,1) ∪ (1, ∞) b) find the equation of the vertical asymptote(s) 𝑥 = −7 𝑥 = 1 c) find the equation of the horizontal asymptote 𝑦 = 0 d) find the x- intercept (14,0) e) find the y-intercept (0,2) 𝑥−4 7) 𝑓(𝑥) = 𝑥 2 −11𝑥−12 Use the graph of 𝑓(𝑥) the function to find the following, then confirm your answer using Algebra. a) find the domain, express your answer using interval notation (−∞, −1) ∪ (−1,12) ∪ (12, ∞) b) find the equation of the vertical asymptote(s) 𝑥 = −1 𝑥 = 12 c) find the equation of the horizontal asymptote 𝑦 = 0 d) find the x- intercept (4,0) 1 3 e) find the y-intercept (0, ) 9) 𝑓(𝑥) = 𝑥 2 +5𝑥−6 𝑥+3 Use the graph of 𝑓(𝑥) the function to find the following, then confirm your answer using Algebra. a) find the domain, express your answer using interval notation (−∞, −3) ∪ (−3, ∞) b) find the equation of the vertical asymptote(s) 𝑥 = −3 c) find the equation of the SLANT asymptote 𝑦 = 𝑥 + 2 d) find the x- intercept e) find the y-intercept (−6,0) (−1,0) 11) 𝑓(𝑥) = 𝑥 2 −6𝑥−16 𝑥−2 Use the graph of 𝑓(𝑥) the function to find the following, then confirm your answer using Algebra.a) find the domain, express your answer using interval notation (−∞, 2) ∪ (2, ∞) b) find the equation of the vertical asymptote(s) 𝑥 = 2 c) find the equation of the SLANT asymptote 𝑦 = 𝑥 − 4 d) find the x- intercept (−2,0) (8,0) e) find the y-intercept (0,8) 13) 𝑓(𝑥) = 𝑥+3 𝑥 2 −9 Find the following: a) equation of the vertical asymptote 𝑥 = 3 1 b) coordinates of the “hole” in the graph of 𝑓(𝑥) (−3, − ) 6 15) 𝑓(𝑥) = 𝑥+2 𝑥 2 −6𝑥−16 Find the following: a) equation of the vertical asymptote 𝑥 = 8 1 b) coordinates of the “hole” in the graph of 𝑓(𝑥) (−2, − ) 10 #17 - 28 For each problem find the following: a) the domain of 𝑓(𝑥) written in interval notation (−∞, 3) ∪ (3, ∞) b) the equation of the vertical asymptote (write none if there is no vertical asymptote) 𝑥 = 3 c) the equation of the horizontal asymptote (write none if there is no horizontal asymptote) 𝑦 = 4 d) the equation of the slant asymptote (write none if there is no slant asymptote) NONE e) write the coordinates of any “hole” (write none if there is no hole) NONE f) x- intercept(s) if any (−3,0) g) y-intercept(s) if any (0, −4) h) Sketch a graph of the function 17) 𝑓(𝑥) = 4𝑥+12 𝑥−3 For each problem find the following: a) the domain of 𝑓(𝑥) written in interval notation (−∞, −6) ∪ (−6, ∞) b) the equation of the vertical asymptote (write none if there is no vertical asymptote) 𝑥 = −6 c) the equation of the horizontal asymptote (write none if there is no horizontal asymptote) 𝑦 = 3 d) the equation of the slant asymptote (write none if there is no slant asymptote) NONE e) write the coordinates of any “hole” (write none if there is no hole) NONE f) x- intercept(s) if any (4,0) g) y-intercept(s) if any (0, −2) h) Sketch a graph of the function 6𝑥−24 19) 𝑓(𝑥) = 2𝑥+12 For each problem find the following: a) the domain of 𝑓(𝑥) written in interval notation (−∞, −7) ∪ (−7,1) ∪ (1, ∞) b) the equation of the vertical asymptote (write none if there is no vertical asymptote) 𝑥 = −7 𝑥 = 1 c) the equation of the horizontal asymptote (write none if there is no horizontal asymptote) 𝑦 = 0 d) the equation of the slant asymptote (write none if there is no slant asymptote) NONE e) write the coordinates of any “hole” (write none if there is no hole) NONE f) x- intercept(s) if any (14,0) g) y-intercept(s) if any (0,2) h) Sketch a graph of the function 𝑥−14 21) 𝑓(𝑥) = 𝑥 2 +6𝑥−7 For each problem find the following: a) the domain of 𝑓(𝑥) written in interval notation b) the equation of the vertical asymptote (write none if there is no vertical asymptote) 𝑥 = −5 c) the equation of the horizontal asymptote (write none if there is no horizontal asymptote) 𝑦 = 0 d) the equation of the slant asymptote (write none if there is no slant asymptote) NONE 1 e) write the coordinates of any “hole” (write none if there is no hole) (5, 10) f) x- intercept(s) if any NONE 1 g) y-intercept(s) if any (0, 5). h) Sketch a graph of the function 23) 𝑓(𝑥) = 𝑥−5 𝑥 2 −25 For each problem find the following: a) the domain of 𝑓(𝑥) written in interval notation (−∞, 4) ∪ (4, ∞) b) the equation of the vertical asymptote (write none if there is no vertical asymptote) 𝑥 = 4 c) the equation of the horizontal asymptote (write none if there is no horizontal asymptote) NONE d) the equation of the slant asymptote (write none if there is no slant asymptote) 𝑦 = 𝑥 + 10 e) write the coordinates of any “hole” (write none if there is no hole) NONE f) x- intercept(s) if any (−8,0) (2,0) g) y-intercept(s) if any (0,4) h) Sketch a graph of the function 25) 𝑓(𝑥) = 𝑥 2 +6𝑥−16 𝑥−4