1.10 Rational Functions and Holes

In the context of rational functions, what does a 'hole' in the graph represent?

• A point where the function intersects the x-axis

  
  

• A point where the function has a maximum

  
  

• A point where the function has a minimum

  
  

• A point where the function is undefined

  
  

When factoring a rational function, what causes a hole in the graph?

• When the numerator is zero

  
  

• When a factor cancels out in both the numerator and the denominator

  
  

• When the denominator is zero

  
  

• When the function has a vertical asymptote

  
  

How can you use a table of values to understand the behavior of a function near a hole?

• By finding the maximum value

  
  

• By observing the values as they get closer to the hole

  
  

• By finding the minimum value

  
  

• By calculating the derivative

  
  

What does it mean when the limit of a function as x approaches a value from the left is negative infinity?

• The function is approaching zero.

  
  

• The function is undefined.

  
  

• The function is decreasing without bound.

  
  

• The function is increasing without bound.

  
  

When approaching a vertical asymptote from the left, if the function goes to negative infinity, what does this indicate?

• The function is decreasing without bound.

  
  

• The function has a hole.

  
  

• The function is undefined.

  
  

• The function is increasing without bound.

  
  

What does the end behavior of a function describe?

• 
  The behavior of the function as y approaches a specific value.

  
  

• The behavior of the function as x approaches infinity or negative infinity.

• The behavior of the function as x approaches a specific value.

  
  

• The behavior of the function as y approaches infinity or negative infinity.

  
  

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

• It makes the function negative.

  
  

• It makes the function equal to zero.

  
  

• It makes the function positive.

  
  

• It makes the function undefined.

  
  

What causes the zeros of a rational function?

• When both numerator and denominator are zero

  
  

• When the numerator is positive

  
  

• When the numerator is zero

  
  

• When the denominator is zero

  
  

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

• It creates an additional zero

  
  

• It has no effect

  
  

• It cancels out the zero

  
  

• It makes the zero undefined

  
  

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

  
  

• Undefined

  
  

• Zero

• Infinity