Quiz on Sketching Graphs of Rational Functions

What is the first step in sketching the graph of a rational function?

• Calculating the derivative

• Drawing the x and y axes

• Identifying asymptotes

• Plotting random points

How do you find the vertical asymptote of a rational function?

• Calculate the limit as x approaches infinity

• Set the numerator equal to zero

• Find the derivative

• Set the denominator equal to zero

What is the y-intercept of the function f(x) = (x - 4) / (x + 2)?

• (-2, 0)

• (2, 0)

• (0, 2)

• (0, -2)

What happens to the y-values as x approaches negative infinity in the first example?

• They approach 2

• They approach 0

• They become undefined

• They approach 1

Why might a calculator graph of a rational function be misleading?

• It connects discontinuous parts of the graph

• It only works for linear functions

• It doesn't show asymptotes

• It always shows a straight line

In the second example, what is the horizontal asymptote?

• y = 1

• y = 0

• x = 1

• x = 0

What is the x-intercept of the function in the second example?

• (0, 0)

• (1, 0)

• (0, 1)

• (2, 0)

Can a rational function cross its horizontal asymptote?

• Yes, but only for small x values

• Yes, always

• No, never

• Yes, but only for large x values

What is the significance of a horizontal asymptote in a rational function?

• It is the minimum value of the function

• It shows the behavior as x becomes very large

• It indicates where the graph starts

• It is the maximum value of the function

What should you do after finding asymptotes and intercepts when sketching a rational function?

• Stop and check your work

• Plot additional points to understand the graph

• Erase the graph and start over

• Draw a straight line through the points