Question

Algebra 2 help please...

Write an equation for a horizontal translation of y = 2/x. Then write an equation for a vertical translation of y = 2/x. Identify the horizontal and vertical asymptotes of the graph of each function.

Answer 1

A horizontal translation is usually accomplished by replacing x by x - h, where the translation is h units.
For the vertical translation, you do a similar thing with y. Replace y with y - k for a transdlation of k units. Since you have y = 2/x, replacing y with y - k, you get
y = 2/x + k
Choose numbers of h and for k.

Answer 2

@mathstudent55 would the vertical translation be y-k=2/x ?

Answer 3

yes. all you need to do is choose a number for k.

Answer 4

@mathstudent55 okay, so if i use 2 for k, how do I find the horizontal and vertical asymptotes?

Answer 5

Do you know how to find the asymptotes of the original function, y = 2/x?

Answer 6

I'm not really sure how you find asymptotes period :/

Answer 7

The asymptotes of a hyperbola of the form
xy = c, where c is a non-zero number,
are the x-axis and the y-axis.

Since the form is xy = c, you can solve for y and get y = c/x

In your case, you have y = 2/x.
For the hyperbola y = 2/x, the asymptotes are the coordinate axes.

Answer 8

Oh okay, so if I was to use 2 for k then would I have to do any math to it? @mathstudent55

Answer 9

When k = 2, the entire graph shifts 2 untis up. So the vertical asymptote remains the same, and the horizontal asymptote becomes the line x = 2, which is a horizontal line 2 units above the x-axis.