# Lesson Worksheet: Horizontal and Vertical Asymptotes of a Function Mathematics • 10th Grade

In this worksheet, we will practice finding the horizontal and vertical asymptotes of a function.

Q1:

Find the vertical and horizontal asymptotes of the function .

• AThe function has no vertical asymptote and a horizontal asymptote at .
• BThe function has no vertical asymptote and a horizontal asymptote at .
• CThe function has a vertical asymptote at and no horizontal asymptote.
• DThe function has no vertical asymptote and a horizontal asymptote at .
• EThe function has a vertical asymptote at and no horizontal asymptote.

Q2:

What are the two asymptotes of the hyperbola ?

• A
• B
• C
• D
• E

Q3:

The graph of equation is a hyperbola only if . In that case, what are the two asymptotes?

• A
• B
• C
• D
• E

Q4:

By writing the expression in the form , determine the asymptotes of .

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q5:

On the left is the graph of and on the right is the graph of . What are the coordinates of the intersection of the asymptotes of ?

• A
• B
• C
• D
• E

Find , , and so that with , we have .

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q6:

Consider the function .

What are the vertical and horizontal asymptotes of the graph ?

• A,
• B,
• C
• D,
• E,

Write in a simplified form. What are the vertical and horizontal asymptotes of the graph ?

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Write in a simplified form. What are the vertical and horizontal asymptotes of the graph ?

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

What combination of horizontal and vertical shifts moves the intersection of the asymptotes of the graph to the origin ?

• Aa shift of to the left and a shift of 2 downward
• Ba shift of to the right and a shift of 2 upward
• Ca shift of to the left and a shift of 2 downward
• Da shift of to the left and a shift of 1 downward
• Ea shift of to the right and a shift of 2 upward

What is the dilation factor required to map the graph of onto the hyperbola ? Write this in the form .

• Aa dilation by a factor of so
• Ba dilation by a factor of so
• Ca dilation by a factor of so
• Da dilation by a factor of so
• Ea dilation by a factor of so

Applying a shift of 1 to the right, a shift of 3 upward, and then a dilation by a factor of 2 to the graph of produces the graph of . What is ?

• A
• B
• C
• D
• E

What sequence of transformations maps the graph of onto the hyperbola ?

• Aa shift of to the right, a shift of downward, and then a dilation by a factor of
• Ba shift of to the right, a shift of downward, and then a dilation by a factor of
• Ca shift of to the right, a shift of downward, and then a dilation by a factor of
• Da shift of to the right, a shift of downward, and then a dilation by a factor of
• Ea shift of to the right, a shift of downward, and then a dilation by a factor of

Q7:

What are the two asymptotes of the hyperbola ?

• A
• B
• C
• D
• E

Q8:

Determine the vertical and horizontal asymptotes of the function .

• AThe vertical asymptote is at , and the horizontal asymptote is at .
• BThe vertical asymptote is at , and the horizontal asymptote is at .
• CThe vertical asymptote is at , and the horizontal asymptote is at .
• DThe function has no vertical asymptote, and the horizontal asymptote is at .
• EThe vertical asymptote is at , and the function has no horizontal asymptote.

Q9:

Find the vertical and horizontal asymptotes of the function .

• AThe function has vertical asymptotes at and and a horizontal asymptote at .
• BThe function has vertical asymptotes at and and no horizontal asymptotes.
• CThe function has vertical asymptotes at and and a horizontal asymptote at .
• DThe function has vertical asymptotes at and and no horizontal asymptotes.
• EThe function has vertical asymptotes at and and a horizontal asymptote at .

Q10:

Find the vertical and horizontal asymptotes of the function .

• AThe function has a vertical asymptote at and a horizontal asymptote at .
• BThe function has a vertical asymptote at and a horizontal asymptote at .
• CThe function has a vertical asymptote at and no horizontal asymptote.
• DThe function has a vertical asymptote at and no horizontal asymptote.
• EThe function has a vertical asymptote at and a horizontal asymptote at .

This lesson includes 6 additional questions and 45 additional question variations for subscribers.