1. [-/5.88 Points] DETAILS SALGTRIG4 3.6.009. A rational function is given. r(x) = - X - 6 (a) Complete each table for the function. (Round your answers to three decimal places where applicable.) Table 1 Table 2 X r(x) X r(x) 5.5 6.5 5.9 6.1 5.99 6.01 5.999 6.001 Table 3 Table 4 X r(x) X r(x) 10 -10 50 -50 100 -100 1000 -1000 (b) Describe the behavior of the function near its vertical asymptote, based on Tables 1 and 2. r(x ) - as x - 6- and r(x) - as x * 6+. (c) Determine the horizontal asymptote, based on Tables 3 and 4. y = Need Help? Read It Watch It2. [-/5.88 Points] DETAILS SALGTRIG4 3.6.011. A rational function is given. r(x) = - 3x - 10 (x - 2)2 (a) Complete each table for the function. (Round your answers to three decimal places where applicable.) Table 1 Table 2 X r(x) X r(x) 1.5 2.5 1.9 2.1 1.99 2.01 1.999 2.001 Table 3 Table 4 X r(x) X (x) 10 -10 50 -50 100 -100 1000 -1000 (b) Describe the behavior of the function near its vertical asymptote, based on Tables 1 and 2. r( x ) - as x - 2. (c) Determine the horizontal asymptote, based on Tables 3 and 4. y = Need Help? Read It Watch It3. [-/5.88 Points] DETAILS SALGTRIG4 3.6.013. Use transformations of the graph of y = 1/x to graph the rational function, as in Example 2. X - 5 4 - 4 A 4 2 2 X - X -10 -5 10 -10 -5 10 -2 -2 -4 O O 4 2 2 . X - X 10 5 10 -10 5 WebAssign Plot -2 -2 -4 O State the domain and range. (Enter your answers using interval notation.) domain range Need Help? Read It Watch It4. [-/5.88 Points] DETAILS SALGTRIG4 3.6.017. Use transformations of the graph of y = 1/x to graph the rational function, as in Example 2. t(x) = 2x - 1 x - 1 y LO 10 5 - X -15 -10 -5 5 10 15 15 -10 -5 5 10 15 -5 -5 O -101 O -10 1 4 4 - X -15 -10 -5 5 10 15 -15 - 10 -5 5 10 15 O O State the domain and range. (Enter your answers using interval notation.) domain range Need Help? Read it Watch It5. [45.88 Points] DETAILS SALGTRIGII 3.6.019. Use transformations of the graph of y - 11x to graph the rational function, as In Example 2. roe: - State the domain and range. [Enter your answers using interval notation.) domain range Need Help? 6. [-/5.88 Points] DETAILS SALGTRIG4 3.6.021.MI. Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DNE.) r(x) = x - 5 x +8 x-intercept (x, y) = y-intercept ( x, y ) = Need Help? Read It Watch It Master It 7. [-/5.88 Points] DETAILS SALGTRIG4 3.6.025.MI. Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DNE.) r(x ) = x - 16 x2 x-intercept ( x, y ) = (smaller x-value) x-intercept (x, y ) = (larger x-value) y-intercept (x, y) =( Need Help? Read It Watch It Master It8. [-/5.88 Points] DETAILS SALGTRIG4 3.6.027. From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.) x-intercept ( x, y ) = y-intercept ( x, y ) = vertical asymptote horizontal asymptote 4 5- -X -10 -5 5 10 -5 10 Need Help? Read It Watch It 9. [-/5.88 Points] DETAILS SALGTRIG4 3.6.031. Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.) r(x) = - 9 x - 5 vertical asymptote(s) horizontal asymptote Need Help? Read It Watch It10. [-/5.88 Points] DETAILS SALGTRIG4 3.6.033. Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.) r( x) = - 4x + 1 16x2 + 1 vertical asymptote(s) horizontal asymptote Need Help? Read It 11. [-/5.88 Points] DETAILS SALGTRIG4 3.6.037. Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.) "(x) = (x + 1) (3x - 5) (x - 3)(6x + 9) vertical asymptote(s) horizontal asymptote Need Help? Read It 12. [-/5.88 Points] DETAILS SALGTRIG4 3.6.041. Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.) t ( x) = x + 2 x - 3 vertical asymptote(s) horizontal asymptote Need Help? Read It Watch ItFind the intercepts and asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.) r(x) = 4x - 4 x+ 2 x-intercept (x, y) = ( y-intercept ( x, y ) = ( vertical asymptote(s) horizontal asymptote Sketch a graph of the rational function. 120 10 15 10 5 X 15 -10 -5 10 15 -5 -10 15 -10 -5 5 10 15 -15 O O .20 20 15 101 - 15 -10 -5 5 10 15 -10 -15 - 10 -5 5 10 15 -15 O State the domain and range. Use a graphing device to confirm your answer. (Enter your answers using interval notation.) domain rangeFind the intercepts and asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.) r(x) = _x + 4x - 6 X2 - 4x + 4 x-intercept (x, y) = ( y-intercept ( x, y ) = vertical asymptote(s) I asymptote Sketch a graph of the rational function. 10 |10 10- 5- -10 -5 5 10 O -10 :- 10 4 2 4 10 1 10 .10 10 10- L X -5 O 10- O 10 - State the domain and range. Use a graphing device to confirm your answer. (Enter your answers using interval notation.) domain ranger(x)= X2 - 6x + 9 x2 + 6x + 9 x-intercept (x, y ) = ( y-intercept (x , y ) = ( vertical asymptote(s) asymptote Sketch a graph of the rational function. Y 10 15 220---sym--4- -30 -20 - 10 20 30 +5 -10 O O 15 15 10 10 5 30---220 ---210---- -+---10----20 30 30 . 20 . 10 10 20 30 -10 -10 O -15 O -15 State the domain and range. Use a graphing device to confirm your answer. (Enter your answers using interval notation.) domain anger(x) = x - 3x - 4 x + 1 x-intercept (x, y ) = ( y-intercept (x, y) = ( vertical asymptote(s) horizontal asymptote Sketch a graph of the rational function. y 24 10 - 10/ 5/ 5 -10 -5 10 -10 -5 5 - X 10 -5 O - 10/ O - 10 24 y 10 10 5 -10 - 5 X 10 -10 X 5 10 5 -5 -101 O -101 State the domain and range of the function. (Enter your answers using interval notation.) domain range17. [-/5.92 Points] DETAILS SALGTRIG4 3.6.067. Find the factors that are common in the numerator and the denominator. Then find the intercepts and asymptotes. [Hint: Check that x + 1 is a factor of the numerator.] (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.) r(x) = x - 9x2 + 15x + 25 x+ 1 x-intercept ( x, y) = ( y-intercept (x, y ) = ( vertical asymptote(s) horizontal asymptote Sketch a graph of the rational function. y - 4 40 -10 - 5 5 10 10 30 -20 20 -30 10 -40 X O -10 -5 5 10 - 4 40 -10 -5 10 30 -10 20 -20 10 -30 - X -A40 -10 10 C State the domain and range of the function. (Enter your answers using interval notation.) domain range Need Help? Read It