Identify Rational Function

What is the horizontal asymptote? 

• x = 2

• x = 7

• y = 2

• y = 7

Identify the parent function of the graph.

• Rational

• Cubic

• Exponential

• Sine

What is a vertical asymptote in a rational function?

• A vertical asymptote is a curve where the function has a local maximum.

• A vertical asymptote in a rational function is a vertical line where the function approaches positive or negative infinity as the input approaches a certain value.

• A vertical asymptote is a point where the function is undefined.

• A vertical asymptote is a horizontal line where the function approaches infinity.

How can you determine the equation of a vertical asymptote in a rational function?

• Set the numerator of the rational function equal to zero and solve for the variable

• Divide the numerator by the denominator of the rational function

• Find the average of the numerator and denominator of the rational function

• Set the denominator of the rational function equal to zero and solve for the variable.

How do you identify asymptotes in a rational function?

• Horizontal asymptotes are determined by comparing the degrees of the numerator and the constant term

• Asymptotes occur at values that make the numerator zero

• Vertical asymptotes occur at values that make the denominator zero, and horizontal asymptotes are determined by comparing the degrees of the numerator and denominator.

• Vertical asymptotes occur at values that make the numerator zero

Explain the process of graphing a rational function with vertical asymptotes.

• Identify vertical asymptotes, plot them as dashed lines, and analyze function behavior around them.

• Connect asymptotes with straight lines to form the graph.

• Ignore asymptotes and focus on the x-intercepts only.

• Identify horizontal asymptotes and plot them as solid lines.

Describe the steps involved in graphing a rational function with horizontal asymptotes.

• Draw the vertical asymptotes first

• Ignore the horizontal asymptotes

• Use only one horizontal asymptote as a reference

• Graph the rational function using the horizontal asymptotes as guidelines.

What is the significance of asymptotes in understanding the behavior of rational functions?

• Asymptotes provide information about how a rational function behaves near certain values, such as where it approaches infinity or becomes undefined.

• Asymptotes are always present in linear functions

• Asymptotes are only relevant for irrational functions

• Asymptotes have no impact on rational functions

What are the conditions for a rational function to have a horizontal asymptote?

• The degree of the numerator is less than the degree of the denominator.

• The function has a vertical asymptote

• The function has a hole at the asymptote

• The function has a slant asymptote

Discuss the role of asymptotes in determining the end behavior of rational functions.

• Asymptotes have no impact on the end behavior of rational functions

• Asymptotes determine the exact values of rational functions at all points

• Asymptotes only affect the behavior of rational functions in the middle range of input values

• Asymptotes play a crucial role in predicting the behavior of rational functions as the input values become extremely large or small.