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## TOP RATIONAL FUNCTIONS QUESTIONS

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Give an example of a rational function whose graph has two vertical asymptotes: ​x​ = 2 and ​x​ = 7. Explain how you know that these are vertical asymptotes.

Which of the following functions is shown in the graph below?

Which of the following functions is shown in the graph below?

Which of the following functions is shown in the graph below?

Which of the following graphs shows the function below? f left parenthesis x right parenthesis space equals space fraction numerator x squared minus 2 x space minus space 15 over denominator x minus 5 end fraction

Identify vertical asymptotes in the function below. f left parenthesis x right parenthesis space equals space fraction numerator x squared minus space 8 x space plus space 7 over denominator x squared plus 2 x space minus space 3 end fraction

Identify all holes in the function below. f left parenthesis x right parenthesis space equals space fraction numerator x squared minus 4 x space minus space 5 over denominator x squared plus 3 x space plus space 2 end fraction

Identify the equations of the vertical asymptotes of the following function. f left parenthesis x right parenthesis space equals fraction numerator 3 over denominator x squared minus 7 x space plus space 10 end fraction

Which of the following functions has a graph with a slant asymptote?

What is the horizontal asymptote of the graph of the following function? y equals fraction numerator 10 x squared minus 1 over denominator x cubed plus 8 end fraction

Which of the following functions is graphed below?

In your own words, explain how to find the asymptotes of a rational function in the form

You paid \$120 for a membership to a racquetball club. Court time is \$4 per hour. Write a model that represents your average cost per hour of court time as a function of the number of hours played. What is the horizontal asymptote of this model and what do

You paid \$120 for a membership to a racquetball club. Court time is \$4 per hour. Write a model that represents your average cost per hour of court time as a function of the number of hours played.

Which of the following graphs shows the function below? y equals fraction numerator 2 over denominator x minus 3 end fraction plus space 1

Which of the following graphs shows the function below? y equals fraction numerator 6 over denominator x plus 2 end fraction minus 6

Which of the following graphs shows the function below? f left parenthesis x right parenthesis space equals space fraction numerator 2 x over denominator x minus 1 end fraction

Which of the following graphs shows the function below? f left parenthesis x right parenthesis space equals space fraction numerator x plus 2 over denominator x minus 1 end fraction space

Find the horizontal asymptote of the function below: y equals fraction numerator 2 x minus 8 over denominator x minus 5 end fraction

Find the horizontal asymptote of the function below: y equals fraction numerator negative 2 over denominator x minus 4 end fraction minus 3

Find the vertical asymptote of the function below: y equals fraction numerator 2 x plus 2 over denominator 3 x minus 1 end fraction

Find the vertical asymptote of the function below: y equals fraction numerator 3 over denominator x plus 1 end fraction minus 2

In your own words, explain the difference between multiplying rational expressions and dividing rational expressions. In our definition of division for P over Q divided by R over S , we stated that Q not equal to 0 comma S not equal to 0 comma a

The total revenue from the sale of a popular book is approximated by the rational function R(x) = fraction numerator 1000 x squared over denominator x squared plus 4 end fraction, where x is the number of years since publication and R(x) is the total reve

Find g(-2) for the function below. g(x) = fraction numerator x squared plus 8 over denominator x cubed minus 25 x end fraction

Divide the rational expression and simplify. fraction numerator x squared minus 4 over denominator 3 x plus 6 end fraction divided by fraction numerator 2 x squared minus 8 x plus 8 over denominator x squared plus 4 x plus 4 end fraction

Multiply the rational expressions and simplify. fraction numerator 18 a space minus space 12 a squared over denominator 4 a squared plus 4 a space plus space 1 end fraction cross times fraction numerator 4 a squared plus 8 a space plus space 3 over denom

Divide the rational expressions and simplify. fraction numerator x minus 4 over denominator 2 x minus 1 end fraction divided by fraction numerator x squared minus 16 over denominator 2 x minus 1 end fraction

Multiply the rational expressions and simplify. fraction numerator 3 x squared plus 2 x minus 1 over denominator 4 x minus 2 end fraction cross times fraction numerator 3 x minus 2 over denominator 2 x squared plus x minus 1 end fraction

Simplify the expression. fraction numerator p squared minus 8 p plus 15 over denominator p squared minus 6 p plus 9 end fraction

Simplify the expression. fraction numerator 4 b squared minus 16 over denominator b plus 2 end fraction

Find the domain of the rational function. R(x) = fraction numerator 3 plus 2 x over denominator x cubed plus x squared minus 2 x end fraction

Find the domain of the rational function. g(x) = fraction numerator 4 minus 3 x over denominator 2 end fraction

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Rational Functions