Rational functions and asymptotes Practice

{"questions":[{"content":"Fluency: solve x − 7 = 0 for the excluded value. [[input-rat-t1]]","widgets":{"input-rat-t1":{"type":"input","answer":"7"}},"hints":["Set the factor to zero."],"explanation":"The excluded value is x = 7."},{"content":"Method recognition: numerator degree 3 and denominator degree 2. What should you do for end behavior?<br>[[choice-rat-t2]]","widgets":{"choice-rat-t2":{"type":"choice","options":["Polynomial division","Use a normal CDF","Apply induction","Find a median"],"answer":[0],"explanations":["Division identifies the oblique asymptote.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again."]}},"hints":["The degree difference is one."],"explanation":"Division identifies the oblique asymptote."},{"content":"Exam execution: which statement correctly reports a vertical asymptote?<br>[[choice-rat-t3]]","widgets":{"choice-rat-t3":{"type":"choice","options":["x = 2","2","(2, 0)","y approaches 2 horizontally"],"answer":[0],"explanations":["A vertical asymptote must be written as x = constant.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again."]}},"hints":["An asymptote is a line."],"explanation":"A vertical asymptote must be written as x = constant."},{"content":"Synthesis: a graph seems to cross a predicted vertical asymptote. What should you do?<br>[[choice-rat-t4]]","widgets":{"choice-rat-t4":{"type":"choice","options":["Recheck factor cancellation and the graphing window","Accept the display without algebra","Delete the denominator","Round all coefficients"],"answer":[0],"explanations":["A cancelled factor or unsuitable display window may explain the picture.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again."]}},"hints":["Use algebra to classify the discontinuity."],"explanation":"A cancelled factor or unsuitable display window may explain the picture."},{"content":"What should you do next after finding excluded denominator values?<br>[[choice-rat-t5]]","widgets":{"choice-rat-t5":{"type":"choice","options":["Factor and test whether each factor cancels","Differentiate three times","Use inverse normal","Assume every value is an asymptote"],"answer":[0],"explanations":["Cancellation determines the type of discontinuity.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again."]}},"hints":["Distinguish holes from asymptotes."],"explanation":"Cancellation determines the type of discontinuity."}],"mix":1}