solve questions 1,5,and 9 for the rational inequalities image. and do the work and show it all on paper

Rational Inequalities Date Period Solve each inequality. 1 ) x - 7 x - 1 2) x+5 x- 4 3) x + 32 $3 x + 68 x+6 4) -25 x+8 5 ) (x+ 3)(x+5). - 20 x + 6 x+2 6) x2 - 5x - 24 -20 10 7) 11 3 8) - - 4 x- 5 x - 6 x + 7 x+8 7 8 9) *+5 x+6 10 ) ( x + 7)(x - 3) , 0 ( x - 5 ) 23.10 Homework 1. The rational function r is given by r(a) = ty. For what values of a does r(a) = 0? (A) = -2.303 and x = 1.000 only (B) x = -1.643 and x = 1.144 only (C) = = -2.303, x = 1.000, and x = 1.303 only (D) = -2.303, x = -1.643, x = 1.000, x = 1.303, and x = 1.144 2. The rational function r is given by r(x) = 2+4 1'+4x2 +4x . On what intervals of x is r() 2 0? (A) x20 (B) -3 3 only (D) -3 3 3. The rational function f is given by f(x) = 2(2-1)(243) 2+2x-5 , where k is a positive integer. For which of the following values of k will the graph of f have a horizontal asymptote at y = 0? (A) 2 3 (C) 4 (D) 5 4. The function h is given by h(x) = 25 7-T. Which of the following statements is true? (A) h is equivalent to 2-12 and has the same end behavior as the graph of y = 2x. (B) h is equivalent to 2 3 and has the same end behavior as the graph of y = 2x. (C) h is equivalent to " + 4 - and has the same end behavior as the graph of y = 212. (D) h is equivalent to -31-3 2x2-2x-12 and has the same end behavior as the graph of y = 2x. 5. The rational function h is expressed as the quotient of two polynomial functions f and g by h(x) = 2. The function f is given by f(x) = 6x3 - x2 + 60x - 25. If the graph of h has a slant asymptote of y = 2x - 1, which of the following describes g ? (A) g has degree 2 with leading coefficient 3. (B) g has degree 2 with leading coefficient 12. (C) g has degree 3 with leading coefficient 3. (D) g has degree 4 with leading coefficient 12. 6. The rational function h is given by h(a) = 21 3x2-21+7 2x5 +5x-2:2-13 . Which of the following describes the end behavior of h ?3.10 Homework (A) As x increases without bound, h(x) increases without bound, and as ax decreases without bound, h(a) decreases without bound. (B) As T increases without bound, h() increases without bound, and as x decreases without bound, h(x) increases without bound. (C) As ar increases without bound, h() decreases without bound, and as x decreases without bound, h() increases without bound. (D) As c increases without bound, h( ) decreases without bound, and as a decreases without bound, h(x) decreases without bound. 7. - NW T - W - N 4-3-2-10 2 - 3 - 2 x -2- -2- -3- -4+ -4+ Graph of f Graph of g The graphs of the polynomial functions f and g are shown. The function h is defined by h(a) = 18) g(x) ' . What are all vertical asymptotes of the graph of y = h(x) ? (A) = = 2 only (B) c = 3 only (C) = -2 and x = 3 only (D) x= -2, x = 2, and x = 39. 'Which of the following names a function with a hole in its graph at a: = 1 and provides correct reasoning related to the hole? 3.10 Homework (A) The graph of f (x) = 1-1 I has a hole at (1, 2) because the values of get arbitrarily close to 2 for a -values sufficiently close to 1, but the function is undefined at a = 1. (B) The graph of g(a) = has a hole at a = 1 because the values of increase without bound for I -values arbitrarily close to 1. (C) The graph of h(2) = 1-+1 Ar 4 has a hole at (1, 0) because the values of 45-4 +1 are arbitrarily close to 0 for a -values sufficiently close to 1. The graph of k(x) = -has a hole at x = 1 because the values of 4x - 4 and (x - 1) are (D) arbitrarily close to 0 for x-values sufficiently close to 1. 10. r(x) 1.997 1.3337 1.998 1.3336 1.999 1.3334 2.001 1.3332 2.002 1.3331 2.003 1.3330 The rational function r is given by r(x) = 4 72_x-2 . The table gives values of r(x) for selected values of x. Which of the following statements is true? (A) lim r(x) = 3, so r(2) = 3. (B) 1-+2 lim r(x) = = and r is undefined at a = 2, so the graph of r has a hole at (2, ). (C) lim r(x) = 2 and r is undefined at a = 2, so the graph of r has a hole at (2, ). (D) x-+2+ lim r(x) = co, lim r(x) = oo, and r is undefined at a = 2, so the graph of r has a vertical asymptote at x = 2.1 The rational fonction o. Given 8 (OC ) = 20 3- 4 2+ 3 20 4 + 2x - 4 Let's check for the options below: aJoc = - 2. 303 7 ( - 2 . 303 ) = ( 2. 303 ) 3 - 4 ( - 2 . 303 ) + 3 2. 303)4 - 2 ( - 2, 303 ) - 4 - 12 . 212 + 9. 212 + 3 2 O 28. 13 - 4 606 - 4 19:52 O ,: 20 = -2.303 is correct to satisfy 8 ( c ) = 0. 6. ) OC = 1 o ( 1 ) = 13 - 4 ( 1) + 3 14 - 2 ( 1) - 4 2 1 - 4+ 3 1-2 - 4 = 0 . 2= 1 is comect ( ) 20 = 1. 14 4 ~ ( 1. 164 ) = (1. 144) 3 - 4 (1- 144) + 3 2 1. 497 - 4.5-76 + 3 (1.14ce)4- 2 (1. 14 4) = 4 1. 712 + 2. 288 - 4 = - 0.079 0 Any number divided by zero is infinity . = 1.14 4 is wrong and does not safify the o ( x) = 0.d ) 2C = 1, 303 8 ( 1 - 303 ) 2 ( 1. 303 ) 5 - 4 ( 1 - 303 ) + 3 ( 1.303)4 + 2 ( 1, 303 ) 4 - 4 8, 212 - 5- 212 + 3 O Zz 2 88 2 + 2. 606 - 4 1. 488 10 .: 2=1:303. is correct for 8 ( De ). = 0. fence, the option 3 is correct. X 2 - 2.303, 2 = 1.000, & 20 = 1, 303 only 2 Given 8 ( 20 ) = 20 3 + 41 52 2 + 4 20 2C 2 - 9