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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 .

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