Rational Functions Quiz

Which statement best describes a rational function?

• A rational function is a function that can be written as the sum of two polynomials.

• A rational function is a function that can be written as the product of two polynomials.

• A rational function is a function that can be written as the ratio of two polynomials.

• A rational function is a function that can be written as the difference of two polynomials.

Which feature is commonly found in the graph of a rational function?

• The graph of a rational function often has vertical asymptotes where the denominator equals zero.

• The graph of a rational function always passes through the origin.

• The graph of a rational function is always a straight line.

• The graph of a rational function never has horizontal asymptotes.

What happens in the table of values for f(x)=1x at x=0?

• If a rational function is given by f(x)=1x, its table of values will show undefined values where x=0.

• If a rational function is given by f(x)=1x, its table of values will show undefined values where x=1.

• If a rational function is given by f(x)=1x, its table of values will show undefined values where x=−1.

• If a rational function is given by f(x)=1x, its table of values will show undefined values where x=2.

Why is f(x)=x+2x−3 considered a rational function?

• The equation f(x)=x+2x−3 is not a rational function because the numerator is not a polynomial.

• The equation f(x)=x+2x−3 is not a rational function because the denominator is not a polynomial.

• The equation f(x)=x+2x−3 is not a rational function because it is not a ratio.

• The equation f(x)=x+2x−3 is a rational function because both the numerator and denominator are polynomials.

Which of the following is true about representing rational functions?

• A rational function can only be represented by a graph.

• A rational function can only be represented by an equation.

• A rational function can only be represented by a table of values.

• A rational function can be represented by a table of values, a graph, or an equation.

What are the asymptotes of the graph of f(x)=1x?

• The graph of f(x)=1x has a vertical asymptote at y=0 and a horizontal asymptote at x=0.

• The graph of f(x)=1x has no asymptotes.

• The graph of f(x)=1x has a vertical asymptote at x=1 and a horizontal asymptote at y=1.

• The graph of f(x)=1x has a vertical asymptote at x=0 and a horizontal asymptote at y=0.

How can a table of values be useful when analyzing a rational function?

• A table of values for a rational function always shows a constant rate of change.

• A table of values for a rational function only shows positive values.

• A table of values for a rational function helps to identify points where the function is undefined.

• A table of values for a rational function never shows asymptotes.

Why is f(x)=x2−1x+1 a rational function?

• The equation f(x)=x2−1x+1 is a rational function because both the numerator and denominator are polynomials.

• The equation f(x)=x2−1x+1 is not a rational function because the numerator is not a polynomial.

• The equation f(x)=x2−1x+1 is not a rational function because the denominator is not a polynomial.

• The equation f(x)=x2−1x+1 is not a rational function because it is not a ratio.

When does a rational function have a hole in its graph?

• A rational function may have holes in its graph where both the numerator and denominator are zero at the same value of x.

• A rational function never has holes in its graph.

• A rational function always has holes at every integer value of x.

• A rational function has holes only when the numerator is zero.

At which value of x is the graph of f(x)=2xx−4 undefined?

• The graph of f(x)=2xx−4 will be undefined at x=4.

• The graph of f(x)=2xx−4 will be undefined at x=2.

• The graph of f(x)=2xx−4 will be undefined at x=0.

• The graph of f(x)=2xx−4 will be undefined at x=−4.