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 .

- A The function has no vertical asymptote and a horizontal asymptote at .
- B The function has a vertical asymptote at and no horizontal asymptote.
- C The function has a vertical asymptote at and no horizontal asymptote.
- D The function has no vertical asymptote and a horizontal asymptote at .
- E The function has no vertical asymptote and a horizontal asymptote at .

**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: **

Which of the following lines is a vertical asymptote of the graph of the function ?

- A
- B
- C
- D

**Q7: **

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 left and a shift of 1 downward
- Ca shift of to the left and a shift of 4 downward
- Da shift of to the left and a shift of 1 downward
- Ea shift of to the left and a shift of 3 downward

What is the dilation factor *A* 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 *g*?

- 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

**Q8: **

By sketching a graph, find the vertical asymptotes of the function .

- A ,
- B ,
- C ,
- D ,

**Q10: **

Determine the vertical and horizontal asymptotes of the function .

- A The vertical asymptote is at , and the horizontal asymptote is at .
- B The vertical asymptote is at , and the horizontal asymptote is at .
- C The function has no vertical asymptote, and the horizontal asymptote is at .
- D The vertical asymptote is at , and the horizontal asymptote is at .
- E The vertical asymptote is at , and the function has no horizontal asymptote.