Question

20. What affect does h = 4 have on the parent function y = 1/x

A. Graph moves 4 units up
B. Vertical stretch by a factor of |4|
C. Graph moves 4 units to the right
D. Graph moves 4 units left

Answer 1

Where is 'h?'

Answer 2

"What affect does h = 4 have on the parent function y = 1/x"

Where can I find this 'h' that you're asking about?

Answer 3

How long have you been studying this topic? Are you sure you haven't seen other formulas that have an 'h' in them?

Answer 4

There is a standard formula that I know
\[\large y=\frac{a}{x-h}+k\]
but I want to make sure that's the same one that applies here.

Answer 5

y=1/x is what you get if a=1, and h=k=0.

Answer 6

Ah, ok, well that form is pretty standard in mathematics, so I guess it's the right one.
In that case, an h=4 causes a horizontal shift.
The best way for you to see this is to graph both y=1/x and y=1/(x-4) and see what the transformation looks like.

Answer 7

Yes. It is similar to a quadratic in vertex form
y=a(x-h)^2+k where 'h' is also a horizontal translation.

Answer 8

Should post this as a new question . . .

Answer 9

Ok, so look again at the standard equation
y=a/(x-h)+k
All else being equal, and only changing y=1/x to y=3/x, what do you suppose will happen to y?

Answer 10

Maybe think of it like this:
y=f(x)=1/x
3/x = 3*f(x).

Answer 11

Right, because all the y's are being multiplied by 3.

Answer 12

(and y is the vertical direction, yes?)

Answer 13

Make sense?

Answer 14

Wonderful! Thank you.
While we're on the subject, what do you suppose happens if you change 'k'?

Answer 15

Use the same reasoning as before. Assume everything else is the same, but now you have y=1/x +k...
The 1/x part stays the same, so the change is y=(same as before)+k.

Answer 16

Yes, but in which direction?

Answer 17

What is being added to, x or y?