quiz 6

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Utah State University *

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1050

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Mathematics

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Apr 3, 2024

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I Quiz Week 6 Name: _Q___,;,,__,:,t,4,11-'-n--'---""'()_' .... ; ..... t/1An_ .... ; .... (l_1 __ Spring 2024 um: -=-U_t_'-1_6 L_1-_7-_J ___ _ By submitting this quiz you are agreeing to follow the rules and expectations described in the "Quiz and Exam Guidelines" pdf. Total points possible: 50 1. Consider rational function /(x) = 2 ~+_ 6 3 . (1.1) (6 points) Complete the table for rational function Then use highlighting or circling to demon- strate what part of the function corresponds to the feature and show how the feature is obtained. AJJ. example for the x-intercept has been provided. Feature Value Justification/Work x-interoept( s) ( ordered pair) /(x) - - x+6 24:i;-3 numerator - 0 X + 6 = 0 z=-6 (-6,0) y-intercept ( ordered pair) /(x)= ~+~3 0,-6 G - - - - ___... 2)-/{fJ) -J _.. .3 Vertical Asymptote(s) X'-= J /(z)= ~+63 IX rf I - ( equation of line) - - - 2,4 2'-IX .>t, ! / Z'-f Horizontal Asympt,ote /(:t) = t+6 ____../ ( equation of line) 7=~ jMx-3 2'1,y::) 2'1 Xf °8 (1.2) (1 point) Describe the end behavior of the function and state which feature from the table above it is most closely related to. (Reminder use the notation, As x _, f (x) _ . ) Feature Description Which feature above is it closely related to? End Behavior tPJ-X 7 -00, fexJ 7,~ r., O<J--'f. 7 C>D, f-('Q -1~-i, ' trr~ L,•·~-d? 2. Find the requested information for the given function, showing work to justify how you obt&ined or copying the function and circling the part where you get the information from. I

f(x) = 3x 2 - 18x + 24 :i;2-5z+4 (2.1) (2 points) Rewrite the fraction with a factored numerator and denominator. Answer: '3( x 4 > C x-2) '(_x -() ()C -LI) J [ X -'-1) (x-]-) -- ( x-\) l 'I{-'-/' (2.2) (2 points) Hole (ordered pair notation): [ ¥:,-lf) 3 ( lj__- -i..i, (: 2 Y-1 - J Answer: ) (2.3) (1 point) Vertical Asymptote (equation notation): Answer: K -:J. I (2.4) (1 point} Horizontal or Slant Asymp- tote (equation notation): Answer: (2.5) (1 point) z-intercept(s) (ordered pair notation): (2.6) (1 point) y-intercept (ordered pair no- tation): o - 0 ,i" ---~ Answer: o-on (O/.J (2. 7) (5 points) Sketch the graph, carefully marking intercepts, holes and asymp- totes and showing as much of the graph as poeeible on the grid provided. y/1\ .,. I [? I V . "%. 1 - , ..... - - ti 1/J, , - 6 - - 2 WI J q /' \ \ - • - - .. X -- -- A - C. \ I - 1 f (2.8) (2 points) Analyze your graph. For what z is /(z) < O? (Interval Not&- tion) Answer: (2.9) (1 point) Analy7.e your graph: As z -oo, /(x) J As X 00, /(z) l__ .. J . ' I

3. Find the requested information for the given function, showing work to justify how you obtained or copying the function a.nd circling the pa.rt where you get the information from. -x 2 +5x-4 g(x) = x- 3 (3.1) (3 points) Divide the numerator by the denominator. Show work. Wme the an- swer in the form: . remainder g( x) = quotient + di . VlSOr X-) -x +-2.. Answer: )_ - X + 2 + X:J (3.2} (1 point) Rewrite the fraction with a factored numerator. Answer: (3.3) (1 point) How can you tell this function does not ha; a hol ?: (3.4} (1 point) Vertical Asymptote (Equation Notation): Answer: (3.5} (1 point) Hon,zqntal o~~--- tote ( equation notation): Answer: IA /:: -)Cf 2- (3.6) (2 points) x-intercept(s) (ordered pair notation): ( ( _.£.1) (K-1) }(':-L.f x--, (3.7) (1 point) y-intercept(s) (ordered pair notation): O f-0 -'-! Answer: 0 -J { ()) !:I.) t J (3.8) (5 ~ints) Sketch ____ the __ gra_p_h_, -carefull-_____.y marking intercepts, holes and asymp- totes a.nd showing as much of the graph as posmble on the grid provided. y 'I ~\ •'\ ,,. \ V .. • "' '- "X l ,, '\, ,A I \ ""' I \ I ,,,_ 6 4 2 ''\~ . ' • - - - , " . \ I I') \ "' \ - \ ,, ' A \ ,~ I '- - 'I ' - (3.9) (1 point) Analy7.e your graph: As x -oo, /(x) -~tl As X 00, /(x) 4' f~ X

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4. (5 points) A graph of g(x) is shown. The dotted lines indicate the asymptotes for g. Write the formula for g(x). A 5 . 3 . .. - ,. ...... 0 · 1 \ , \ I \ ""- ...... r-,.. 8 1) , V,A X= J X ~4' tvt-f- -'l 2- Work: c }(-iJ rx f2} -rr [X ~4) (K-J) u(x) = (t-2-J (Kt") (}f--'-f JC K I J 5. (5 point.s) A rational function h(x) has the following properties. Write the formula for h(x). • lt.s domain is (-oo, 0) U (0, 3) U (3, oo). / Work: - • There is a hole with x-coordina.te 5. tr. .J-1 J [);. -2} C tc -1) c~ X-5 • The horizontal asymptote is at y = 4. j • The x-interce~ (-1,0} and (2, 0). • There is no y-intercept. h(x) = (~J-J )(K-L)(~-51 "' ci-)}(t) [x-5 6. {1 point) There is a a lot going on when you graph rational functions. This is a check-list to make sure you got everything and haven't made (common) mistakes Read each item below, check your earlier work, then check it off list. H you have any questions about what an item means, bring those to te discussion group! Check each of the following and write a check mark in each blank after doing so. • / Found they-coordinate of the hole {it's not O!) Wrote the hole in the form (x, y). • / Check that you don't have a vertical asympt.ote if for the same z-value where there is a hole. . When writing the domain, considered both the vertical asymptote(e) and holes (or consider the function before the hole was removed). • Wrote vertical asymptotes in the form z = #- • J Wrote homontal and slant asymptotes in the form y =#or 1J = expression. .I Drew the asymptotes on the graph. Drew the function so that it approaches the asymptotes {watch to roae;ure it doesn't curve away). • Drew the z- and 11- intercepts and hole on the graph (if they exist). Don't have any additional intercepts or holes.

• j Drew all the parts of the function on the graph. (The parts are called "sheets".) 7. Special Word! There's nothing to fill in for this question and it's not worth points ... but after the quiz is graded, look at the feedback in Gradescope to this question to find the special word.

quiz 6

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