Exploring Graphs of Rational Functions

What is the first step in graphing a rational function?

• Find the vertical asymptotes

• Simplify the function

• Find the x and y intercepts

• Plot extra points

How do you find the x-intercept of a rational function?

• Set the denominator to 0

• Set y to 0

• Set the numerator to 0

• Set x to 0

What should you do first before finding intercepts?

• Simplify the function and check for holes

• Plot extra points

• Find the horizontal asymptotes

• Check for vertical asymptotes

What is the horizontal asymptote if the degree of the numerator is less than the degree of the denominator?

• y = 1

• No horizontal asymptote

• y = a/c

• y = 0

If the degrees of the numerator and denominator are equal, how do you find the horizontal asymptote?

• Set y to 0

• Set x to 0

• There is no horizontal asymptote

• Divide the coefficients of the highest degree terms

What happens if the degree of the numerator is greater than the degree of the denominator?

• No horizontal asymptote

• Vertical asymptote at x = 0

• Horizontal asymptote at y = a/c

• Horizontal asymptote at y = 0

How do you find vertical asymptotes?

• Set x equal to zero

• Set y equal to zero

• Set the denominator equal to zero

• Set the numerator equal to zero

What must you label vertical asymptotes as?

• x = number

• x = 0

• y = number

• y = 0

Why is it important to plot extra points in the middle section of the graph?

• To see the shape of the graph and check for breaks in the horizontal asymptote

• To find the y-intercepts

• To find the vertical asymptotes

• To find the x-intercepts

What tool can you use to find extra points for plotting?

• Protractor

• Ruler

• Calculator

• Graph paper