Characteristics of Rational Functions Practice Problems

Horizontal vs Vertical

• Horizontal asymptotes are horizontal lines that stop the graph from approaching some y value. Example: y = 1

• Vertical asymptotes are vertical lines that stop the graph from approaching some x value. Example : x = 3

Multiple Choice

What are the asymptotes?

• x=1, x= 2, y =1, y= 2

• x= 2, x=-2, y = 1

• x=2 y =-1

• x=1 y =2, y =-2

Multiple Choice

What are the asymptotes?

• $$x=-3,\ y=1$$

• $$x=-3,\ y=-1$$

• $$x=1,\ y=-3$$

• $$x=1,\ y=3$$

Multiple Choice

What is the domain and range?

• D : All real number x ≠ -3 R: All real number y≠ 1

• D : All real number x ≠ 1 R: All real number y≠ -3

• D : All real number x ≠ 3 R: All real number y≠ 1

• D : All real number x ≠ -1 R: All real number y≠ 3

Multiple Choice

What is the name of this function?

• Parabola

• Rational Function 

• Ellipse 

• Cubic 

Multiple Choice

What is the definition of an ASYMPTOTE?

• A curved line. 

• A line that only touches the origin. 

• A line that only lives on the first quadrant. 

• A line that a curve approaches, as it heads towards infinity. 

Multiple Choice

What are the asymptotes?

• x=-2 and y=-1

• x=-2 and y=1

• x=2 and y=1

• x=2 and y = -1

Multiple Choice

What are the asymptotes?

• x=1, x= 2, y =1, y= 2

• x= 2, x=-2, y = 1

• x=2 y =-1

• x=1 y =2, y =-2

Multiple Choice

What is the horizontal asymptote of the function given?

• y = 2

• x = 1

• x = 2

• y = -1

Multiple Choice

What are the asymptotes?

• x = -3        y = 1  

• x = 3         y = 1

• x = -3        y = -1

• x = 3         y = -1

Multiple Choice

Which asymptotes are determined by looking at the denominator of a function? 

• vertical

• horizontal

• slant

• none

Multiple Choice

The horizontal asymptote equals zero when:

• the degree of the numerator and denominator are equal

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

• the degree of the numerator is greater than the degree of the denominator

• the numerator equals zero

Multiple Choice

What y value can this graph not reach because of a horizontal asymptote?

• -1

• 1

• 3

• 0

Multiple Choice

What x value can this graph not reach because of a vertical asymptote?

• 1

• -15

• 3

• 15

Multiple Choice

Is there a vertical asymptote for 1/x ?

• yes

• no