Exploring Adding and Subtracting Rational Expressions

What distinguishes a rational function from a reciprocal function?

• Non-zero denominator

• Polynomials in the numerator only

• Constant function behavior

• Linear function transformation

What creates a vertical asymptote in a rational function?

• Both numerator and denominator are equal

• Denominator equals zero

• Numerator equals zero

• Function does not have polynomials

What results in a horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

• y = 0

• y = 1

• No horizontal asymptote

• y = -1

How do holes in the graph of a rational function occur?

• When a factor in the numerator and denominator cancels out

• When the numerator is zero

• When the denominator is zero

• When the function has no asymptotes

What is the role of factoring in graphing rational functions?

• To simplify the function

• To create more asymptotes

• To eliminate all variables

• To determine the function's limits

What does a horizontal asymptote at y = 3 indicate about the function?

• The function crosses the y-axis at 3

• The function approaches y = 3 as x approaches infinity

• The degree of the numerator is three times the denominator

• The function has a root at y = 3

How can you determine the presence of a slant asymptote?

• When the degree of the numerator is less than the denominator

• When there are no polynomials in the function

• When the degrees of the numerator and denominator are equal

• When the degree of the numerator is greater than the denominator

What does the presence of a hole at x = 3 signify in the graph?

• The function crosses the x-axis at 3

• The function has a vertical asymptote at 3

• The function has a maximum at x = 3

• The function has an undefined point at x = 3

How does the calculator display a function with a hole?

• With an open circle

• With a labeled point

• As a dashed line

• As a continuous line

What is indicated by a horizontal asymptote at y = 0?

• The function has no polynomials

• The numerator's degree is greater than the denominator's

• The numerator's degree is less than the denominator's

• The numerator and denominator have the same degree