Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
In this lesson, we will learn how to find the horizontal and vertical asymptotes of given functions.
Q1:
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₯ ?
Q2:
By sketching a graph, find the vertical asymptotes of the function π ( π₯ ) = 2 π₯ + 6 π₯ β 2 π₯ β 3 2 2 .
Q3:
Find the vertical and horizontal asymptotes of the function π ( π₯ ) = 4 ( β π₯ + 5 ) l n l n .
Donβt have an account? Sign Up
