Exploring Excluded Values and Asymptotes in Rational Functions

What does the variable 'a' in a rational function's equation influence?

• The position of the vertical asymptote

• The excluded values of the function

• The orientation and width of the graph

• The position of the horizontal asymptote

What is an excluded value in a rational function?

• A value that can be substituted for any variable

• A value that makes the function reach its maximum

• A value of x that cannot be used because it makes the denominator zero

• A value that defines the slope of the graph

How do you find the excluded value for the function y = 5 / (X - 2)?

• X = 5

• X = -2

• X = 2

• X = 0

For the function y = 2 / (X + 3), what is the excluded value?

• X = -3

• X = 2

• X = 0

• X = 3

If a rational function has a denominator of X - 5, what is the vertical asymptote?

• X = 0

• There is no vertical asymptote

• X = 5

• X = -5

What is a horizontal asymptote?

• A line the graph touches at its highest or lowest point

• A line the graph approaches but never actually touches

• A diagonal line that intersects the graph

• A vertical line that defines the graph's limit

How is the vertical asymptote of a rational function determined?

• By the 'k' value in the equation

• By the 'h' value in the equation X - h

• By setting the numerator equal to zero

• By the variable 'a' in the equation

In the function y = a / (X - h) + k, what does 'k' represent?

• The y-coordinate of the horizontal asymptote

• The x-coordinate of the vertex

• The x-coordinate of the vertical asymptote

• The slope of the graph

What happens to the graph of a rational function as it approaches an asymptote?

• It intersects the asymptote

• It becomes undefined

• It gets infinitely close but never touches the asymptote

• It diverges away from the asymptote

When graphing a rational function, what is the first step in determining its shape?

• Identifying the horizontal and vertical asymptotes

• Plotting points on the graph

• Determining the slope of the graph

• Finding the excluded values