AnswersCMS 2026-2027 NC Math 3 CREDIT RECOVERYRational Functions

Rational Functions — Test Answers

25 verified answers
21
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What are the equations of the asymptotes of the graph of the function f of x is equal to the fraction with numerator 3 x squared minus 2 x minus 1 and denominator x squared plus 3 x minus 10 ?

A
x is equal to negative 2 , x is equal to 5 and y is equal to 3
B
x is equal to 3 , y is equal to negative 5 , and y is equal to 2
C
x is equal to negative 5 , x is equal to 2 and y is equal to 3
D
x is equal to 3 , y is equal to negative 2 , and y is equal to 5
22
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What is the difference? the fraction with numerator x and denominator x squared minus 16 minus the fraction with numerator 3 and denominator x minus 4

A
the fraction with numerator x minus 3 and denominator open paren x plus 5 close paren times open paren x minus 4 close paren
B
the fraction with numerator 2 times open paren x plus 6 close paren and denominator open paren x plus 4 close paren times open paren x minus 4 close paren
C
the fraction with numerator negative 2 times open paren x minus 6 close paren and denominator open paren x plus 4 close paren times open paren x minus 4 close paren
D
the fraction with numerator negative 2 times open paren x plus 6 close paren and denominator open paren x plus 4 close paren times open paren x minus 4 close paren
23

Which graph represents the function f of x is equal to 4 over x ?

A
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches the y-axis as x approaches 0 from the left. Its turning point is near (negative 1 comma 1). The branch on the right approaches the y-axis as x approaches 0 from the right and approaches the x-axis as x approaches infinity from the left. Its turning point is near (1 comma negative 1).
B
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches the y-axis as x approaches 0 from the left. Its turning point is near (negative 2 comma negative 2). The branch on the right approaches the y-axis as x approaches 0 from the right and approaches the x-axis as x approaches infinity from the left. Its turning point is near (2 comma 2).
C
Image with description A line graph on a Cartesian coordinate plane shows a rational function with two separate branches. The x-axis and y-axis are labeled with even integer values from negative 8 to 8. One branch lies in the first quadrant, passing through (1 comma 1) and approaching both axes without touching them. The second branch lies in the third quadrant, passing through (negative 1 comma negative 1) and also approaching both axes asymptotically.
D
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches the y-axis as x approaches 0 from the left. Its turning point is near (negative 2 comma 2). The branch on the right approaches the y-axis as x approaches 0 from the right and approaches the x-axis as x approaches infinity from the left. Its turning point is near (2 comma negative 2).
24

Which expression is equivalent to the fraction with numerator 3 x to the negative 6 power y to the negative 3 power and denominator 15 x squared y to the 10th power ? Assume x is not equal to 0 , y is not equal to 0

A
the fraction with numerator 5 and denominator x to the 12th power y to the 30th power
B
the fraction with numerator 5 and denominator x to the 4th power y to the 7th power
C
the fraction with numerator y to the 7th power and denominator 5 x to the 4th power
D
the fraction with numerator 1 and denominator 5 x to the 8th power y to the 13th power
25

What is the common denominator of y plus the fraction with numerator y minus 3 and denominator 3 in the complex fraction the fraction with numerator y plus the fraction with numerator y minus 3 and denominator 3 and denominator 5 ninths plus 2 over 3 y ?

A
3
B
3 y open paren y minus 3 close paren
C
y times open paren y minus 3 close paren
D
3 y

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