Exploring Rational Functions and Asymptotic Behavior

How can graphing tools assist in solving rational problems?

• By providing exact numerical solutions

• By solving algebraic equations directly

• By generating random guesses

• By visually eliminating incorrect answers

What value of y is not included in the range of a specific function?

• 1

• 8

• 0

• -3

How do you find a vertical asymptote of a function?

• By setting the numerator equal to zero

• By identifying the zeros of the denominator

• By comparing the degrees of the numerator and denominator

• By finding the y-intercept

What indicates a hole in the graph of a function?

• A vertical asymptote

• An undefined value in the function

• A common factor in the numerator and denominator

• A zero in the numerator

What does a non-removable discontinuity indicate on a graph?

• A hole

• A break in the graph

• A continuous line

• A peak

How can you determine the points of discontinuity in a function?

• By identifying the horizontal asymptotes

• By setting the denominator equal to zero

• By finding the maximum value of the function

• By graphing the function on a calculator

When simplifying a rational expression, what must you always consider?

• The sum of all coefficients

• The coefficient of the leading term

• Possible restrictions in the variable

• The highest degree of x

What determines the domain of a function?

• The intercepts on the graph

• The y-values it can take

• The slope of the function

• The x-values it cannot take

What is the effect of a translation on the graph of a function?

• It changes the slope of the graph

• It moves the graph up, down, left, or right

• It modifies the range of the function

• It alters the x-intercepts of the graph

What are the characteristics of a horizontal asymptote based on the degrees of a function?

• It is always at y = 0

• It is found when the degrees of the numerator and denominator are equal

• It exists only if the degree of the numerator is less than the denominator

• It is determined by the highest degree of x in the numerator