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Rational Functions — Test Answers

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What is the vertical asymptote of the function?

x is equal to negative 3

x is equal to negative 2

x is equal to 3

x is equal to 0

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What is the vertical asymptote of the function?

x is equal to negative 2

x is equal to 0

x is equal to 2

x is equal to negative 10

How many extraneous solutions does the equation have? the fraction with numerator 2 m and denominator 2 m plus 3 minus the fraction with numerator 2 m and denominator 2 m minus 3 is equal to 1

Which statement is true about the discontinuities of the function f of x ? f of x is equal to the fraction with numerator x plus 1 and denominator 6 x squared minus 7 x minus 3

There are asymptotes at x is equal to negative 3 halves and x is equal to 1 third .

There are holes at x is equal to negative 3 halves and x is equal to 1 third .

There are asymptotes at x is equal to 3 halves and x is equal to negative 1 third .

There are holes at x is equal to 3 halves and x is equal to negative 1 third .

What is the solution to the equation the fraction with numerator y and denominator y minus 4 minus the fraction with numerator 4 and denominator y plus 4 is equal to the fraction with numerator 32 and denominator y squared minus 16 ?

y is equal to 0

all real numbers

no solution

y is equal to negative 4 and y is equal to 4

Where are the asymptotes for the following function located? f of x is equal to the fraction with numerator 7 and denominator x squared minus 2 x minus 24

x is equal to negative 4 and x is equal to 6

x is equal to 6 and x is equal to 7

x is equal to 4 and x is equal to negative 6

x is equal to negative 4 and x is equal to 7

What is the solution of the fraction with numerator 3 x plus 8 and denominator x minus 4 is greater than or equal to 0 ?

negative 8 thirds is less than or equal to x comma x is less than 4

x is less than or equal to negative 8 thirds or x is greater than 4

negative 8 thirds is less than x comma x is less than 4

x is less than negative 8 thirds or x is greater than 4

How does the graph of g of x is equal to the fraction with numerator 1 and denominator x plus 4 minus 6 compare to the graph of the parent function f of x is equal to 1 over x ?

g of x is shifted 4 units right and 6 units down from f of x .

g of x is shifted 4 units left and 6 units down from f of x .

g of x is shifted 4 units right and 6 units up from f of x .

g of x is shifted 4 units left and 6 units up from f of x .

What is the solution of the fraction with numerator x plus 4 and denominator 2 x minus 1 is less than 0 ?

negative 4 is less than or equal to x comma x is less than or equal to 1 half

negative 4 is less than or equal to x comma x is less than 1 half

negative 4 is less than x comma x is less than or equal to 1 half

negative 4 is less than x comma x is less than 1 half

What is the solution of the fraction with numerator x squared plus x minus 6 and denominator x minus 7 is less than or equal to 0 ?

x is less than negative 3 or 2 is less than x comma x is less than 7

x is less than or equal to negative 3 or 2 is less than or equal to x comma x is less than 7

negative 3 is less than x comma x is less than 2 or x is greater than 7

negative 3 is less than or equal to x comma x is less than or equal to 2 or x is greater than 7

The inverse variation equation shows the relationship between wavelength in meters, x , and frequency, y y is equal to the fraction with numerator 3 times 10 to the 8th power and denominator x What is the wavelength for radio waves with frequency 3 times 10 to the 9th power ?

3 times 10 inverse m

3 times 10 to the 17th power m

9 times 10 to the 17th power m

1 times 10 inverse m

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

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).

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).

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).

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.

Which of the following represents the solution of 3 halves is equal to 3 over 2 x minus 6 over 5 x ?

x is equal to 1 fifth

x is equal to 5 ninths

all real numbers

no solution

Mario makes 6 free throw shots out of his first 10 attempts. What is the least number of consecutive shots Mario must make to increase his overall percentage from 60 percent to at least 70 percent ?

10 shots

14 shots

1 shot

4 shots

The equation cap d is equal to 13 over cap v shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0 ?

The density approaches infinity.

The density approaches 13 .

The density approaches 1 .

The density approaches 0 .

Which graph represents the function f of x is equal to the fraction with numerator 2 x and denominator x squared minus 1 ?

Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals 1 as x approaches negative infinity from the right and approaches negative infinity as x approaches 0 from the left. The branch on the right approaches negative infinity as x approaches 1 from the right and approaches y equals 1 as x approaches infinity from the left.

Image with description A coordinate plane with a graph showing three branches. The branch on the left approaches y equals 2 as x approaches negative infinity from the right and approaches infinity as x approaches negative 1 from the left. The branch in the middle approaches negative infinity as x approaches negative 1 from the right and approaches negative infinity as x approaches 1 from the left. The branch on the right approaches infinity as x approaches 1 from the right and approaches y equals 2 as x approaches infinity from the left.

Image with description A coordinate plane with a graph showing three branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches negative infinity as x approaches negative 1 from the left. The branch in the middle approaches infinity as x approaches negative 1 from the right and approaches negative infinity as x approaches 1 from the left. It has a turning point at the origin. The branch on the right approaches infinity as x approaches 1 from the right and approaches the x-axis as x approaches infinity from the left.

Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals 2 as x approaches negative infinity from the right and approaches negative infinity as x approaches 1 from the left. The branch on the right approaches infinity as x approaches 1 from the right and approaches y equals 2 as x approaches infinity from the left.

Max can mow a lawn in 45 minutes. Jan takes twice as long to mow the same lawn. If they work together, the situation can be modeled by the following equation, where t is the number of minutes it would take to mow the lawn together. 1 over 45 plus 1 over 90 is equal to 1 over t How long will it take Maxine and Jan to mow the lawn together?

135 point 0 minutes

45 point 0 minutes

67 point 5 minutes

30 point 0 minutes

What is the solution set of x over 4 is less than or equal to 9 over x ?

Image with description A number line from negative 7 to 7. A segment connects an open circle at negative 6 to an open circle at 0. An open circle is at 6 with a ray pointing right.

Image with description A number line from negative 7 to 7. An open circle is at negative 6 with a ray pointing left. A segment connects an open circle at 0 to an open circle at 6.

Image with description A number line from negative 7 to 7. A closed circle is at negative 6 with a ray pointing left. A segment connects an open circle at 0 to a closed circle at 6.

Image with description A number line from negative 7 to 7. A segment connects a closed circle at negative 6 to an open circle at 0. A closed circle is at 6 with a ray pointing right.

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 ?

x is equal to negative 2 , x is equal to 5 and y is equal to 3

x is equal to negative 5 , x is equal to 2 and y is equal to 3

x is equal to 3 , y is equal to negative 2 , and y is equal to 5

x is equal to 3 , y is equal to negative 5 , and y is equal to 2

Ted can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. When they work together, the situation can be modeled by the following equation, where t is the number of hours it would take to clear the field together. 1 third plus 1 half is equal to 1 over t How long will it take Ted and Jacob to clear the field together?

2 hours 30 minutes

1 hour 12 minutes

12 minutes

50 minutes

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