Graphing Rational Equations

How do you determine the vertical asymptote(s) of a rational function?

• Calculate the average of the x-intercepts of the function.

• Find the values of x that make the numerator of the function equal to zero.

• Find the values of x that make the denominator of the function equal to zero.

• Look for the x-values where the function is undefined.

Tags

CCSS.HSF-IF.C.7D

What is the significance of a vertical asymptote in graphing rational functions?

• It indicates the x-intercept of the function.

• It represents the values where the function becomes undefined.

• It represents the maximum value of the function.

• It shows the points where the function is continuous.

Tags

CCSS.HSF-IF.C.7D

What does a horizontal asymptote represent in the graph of a rational function?

• It represents the average value of the function

• It represents the behavior of the function as the input values become very large or very small.

• It represents the x-intercept of the function

• It represents the maximum value of the function

Tags

CCSS.HSF-IF.C.7D

How do you find the slant asymptote(s) of a rational function?

• Take the square root of the numerator to find the slant asymptote

• Multiply the numerator by the denominator to find the slant asymptote

• Subtract the denominator from the numerator to find the slant asymptote

• Divide the numerator by the denominator using long division obtain the equation of the slant asymptote.

Tags

CCSS.HSF-IF.C.7D

• (- infinity, -5) U (5, infinity)
• (-infinity, -5) U (-5, 5) U (5, infinity)
• (- infinity, 5) U (5, infinity)
• (- infinity, 25) U (25, infinity)

• y = 2
• y = 1
• y = 0
• There is no EBA

Tags

CCSS.HSF-IF.C.7D

• -1
• 3
• 1
• -3

Tags

CCSS.HSF-IF.C.7D

• x = 1 , x = -5
• x = 1, x = -5/2
• x = -1/2, x = 5
• x = 0 , x = -5/2

Tags

CCSS.HSF-IF.C.7D

• y = 4x - 17
• none
• y = 4x + 23
• x = 5

Tags

CCSS.HSF-IF.C.7D

• x=-1 y = -3
• x=1 y = -3
• x=-1 y =3
• x=1, y=3

Tags

CCSS.HSF-IF.C.7D