Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to find the horizontal and vertical asymptotes of given functions.

Q1:

Find the vertical and horizontal asymptotes of the function π ( π₯ ) = 3 π₯ β 1 5 π₯ + 3 2 2 .

Q2:

What are the two asymptotes of the hyperbola π¦ = 5 π₯ + 1 3 π₯ β 4 ?

Q3:

The graph of equation π¦ = π π₯ + π π π₯ + π is a hyperbola only if π β 0 . In that case, what are the two asymptotes?

Q4:

By writing the expression π π₯ + π π π₯ + π in the form π΄ π π₯ + π + π , determine the asymptotes of 5 π₯ β 1 3 π₯ β 3 + 2 + 1 2 π₯ 1 β 2 π₯ .

Q5:

Find the vertical and horizontal asymptotes of the function π ( π₯ ) = 3 π β 2 π₯ 2 .

Q6:

Find the vertical and horizontal asymptotes of the function π ( π₯ ) = β 2 π₯ 3 + 2 π₯ β 1 5 π₯ 2 l n .

Q7:

Find the vertical and horizontal asymptotes of the function π ( π₯ ) = 4 ( β π₯ + 5 ) l n l n .

Q8:

On the left is the graph of π ( π₯ ) = 2 π₯ + 1 3 π₯ + 4 and on the right is the graph of π¦ = 1 π₯ .

What are the coordinates of the intersection of the asymptotes of π¦ = π ( π₯ ) ?

Find π , π , and π so that with π ( π₯ ) = π π₯ , we have π ( π₯ ) = π ( π₯ + π ) + π .

Q9:

Which of the following lines is a vertical asymptote of the graph of the function π ( π₯ ) = π₯ β 8 π₯ + 2 π₯ β 1 5 3 2 ?

Q10:

The function π ( π₯ ) = 3 π₯ β 3 3 π₯ + 8 0 ( π₯ β 3 ) ( π₯ β 5 ) ( π₯ β 7 ) 2 is found to have a vertical asymptote at π₯ = 3 . To which of { β β , + β } do the values of π ( π₯ ) go as π₯ approaches 3 from the left and the right?

Q11:

On the left is the graph of π ( π₯ ) = 7 ( 1 β 2 ) β π₯ , which has a horizontal asymptote. On the right is the graph of π ( π₯ ) = 1 π ( π₯ ) .

What is the value of π΄ ?

List all the asymptotes of π ( π₯ ) = 1 π ( π₯ ) .

Q12:

Consider the function π ( π₯ ) = 4 π₯ + 7 2 π₯ β 5 .

What are the vertical and horizontal asymptotes of the graph π¦ = π ( π₯ ) ?

Write π οΌ π₯ + 5 2 ο in a simplified form. What are the vertical and horizontal asymptotes of the graph π¦ = π οΌ π₯ + 5 2 ο ?

Write π οΌ π₯ + 5 2 ο β 2 in a simplified form. What are the vertical and horizontal asymptotes of the graph π¦ = π οΌ π₯ + 5 2 ο β 2 ?

What combination of horizontal and vertical shifts moves the intersection of the asymptotes of the graph π¦ = π ( π₯ ) to the origin ( 0 , 0 ) ?

What is the dilation factor A required to map the graph of π¦ = π οΌ π₯ + 5 2 ο β 2 onto the hyperbola π¦ = 1 π₯ ? Write this in the form π΄ οΌ π οΌ π₯ + 5 2 ο β 2 ο = 1 π₯ .

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 π ( π₯ ) = π π₯ + π π π₯ + π produces the graph of π¦ = 1 π₯ . What is g?

What sequence of transformations maps the graph of π ( π₯ ) = 5 π₯ β 3 2 π₯ + 1 onto the hyperbola π¦ = 1 π₯ ?

Q13:

By sketching a graph, find the vertical asymptotes of the function π ( π₯ ) = 2 π₯ + 6 π₯ β 2 π₯ β 3 2 2 .

Donβt have an account? Sign Up