justification of reasoning for your choice.a.The domain of the function is,11,.b.The factor (x+ 1) is a non-canceling factor in the numerator ofthe equation ofG(x).c.The degree of the numerator is less than the degree ofthe denominator.

Multiple Choice & Free Response Items for the Pre-AP* Mathematics ClassroomPage 216Mark Sparks © 2014Free Response #7 Grading RubricFree Response Part A–3 points total____1False____1The domain of a rational function is,except for the restricted values of the function.____1From the graph,x=–2 is also a restricted value ofG(x) because there is a hole in the graph whichmeans that the domain should be,11,22,.Free Response Part B–3 points total____1True____1A non-canceling factor in the numerator of a rational function indicates anx–intercept on thegraph of the function.____1The graph ofG(x) has anx–intercept atx=–1 so the factor (x+ 1) should be a non-cancelingfactor in the numerator.Free Response Part C–3 points total____1False____1When the degree of the numerator is less than the degree of the denominator, then the graph ofthe rational function has a horizontal asymptote aty= 0.____1The graph ofG(x) has a horizontal asymptote aty= 1, not aty= 0.Thus, the degree of thenumerator cannot be less than the denominator.

Multiple Choice & Free Response Items for the Pre-AP* Mathematics ClassroomPage 217Mark Sparks © 2014Free Response #8Calculator NOT PermittedPictured to the right is the graph ofG(x), a rational function.Thecoordinates of the hole in the graph are31,2.Determine if thefollowing statements are True or False.Give a completejustification of reasoning for your choice.a.The range of the function is,11,.b.The factor (x–1) is a non-canceling factor in the denominatorof the equation ofG(x).c.The factor (x–2) is a factor that in both the numerator and thedenominator of the equation ofG(x).

Multiple Choice & Free Response Items for the Pre-AP* Mathematics ClassroomPage 218Mark Sparks © 2014Free Response #8 Grading RubricFree Response Part A–3 points total____1False____1The range of this rational function is,except for they–coordinate of the hole in thegraph and theyvalue of the horizontal asymptote.____1Thus, the range should be,11,,3131.Free Response Part B–3 points total____1True____1When the equation of a rational function has a non-canceling factor in the denominator, thenthe graph will have a vertical asymptote at the restricted value associated with that factor.____1The graph has a vertical asymptote atx= 1 which means that the factor causing the asymptotewould be (x–1).Free Response Part C–3 points total____1False____1When a factor is in both the numerator and denominator of the equation of a rational function,then the graph will have a hole at the restricted value associated with that factor.

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Continuous function, Mark Sparks