Exploring Rational Functions and Their Zeros

Why can't the denominator of a rational function be zero?

• It makes the function negative.

• It makes the function positive.

• It makes the function equal to zero.

• It makes the function undefined.

What is the domain of a rational function where the denominator is always positive?

• All positive numbers

• All integers

• All real numbers

• All negative numbers

What causes the zeros of a rational function?

• When both numerator and denominator are zero

• When the numerator is zero

• When the numerator is positive

• When the denominator is zero

If the numerator of a rational function is zero, what is the value of the function?

• Undefined

• Zero

• Negative

• Positive

What happens when factors in the numerator and denominator of a rational function cancel out?

• The function becomes undefined

• A vertical asymptote is created

• A hole is created in the graph

• The function becomes zero

What is the effect of a hole on the zeros of a rational function?

• It creates an additional zero

• It cancels out the zero

• It has no effect

• It makes the zero undefined

What causes a vertical asymptote in a rational function?

• When both numerator and denominator are zero

• When the denominator equals zero and does not cancel out

• When the numerator equals zero

• When the numerator is positive

How do you identify vertical asymptotes in a rational function?

• By finding where both numerator and denominator are zero

• By finding where the numerator is positive

• By finding where the denominator equals zero and does not cancel out

• By finding where the numerator equals zero

What is the horizontal asymptote of a rational function where the highest powers of the numerator and denominator are the same?

• The ratio of the leading coefficients

• Zero

• Undefined

• Infinity

What does a sign table help you determine about a rational function?

• The domain of the function

• The range of the function

• The exact value of the function

• The intervals where the function is positive or negative