Question

Does the following graph represent a direct or inverse variation?

Answer 1

hint: direct variation graphs always go through the origin

Answer 2

so no?

Answer 3

so which one is this graph given?

Answer 4

i mean so its not a direct, so it's an inverse.

Answer 5

can you help me with another?

Answer 6

sure

Answer 7

describe the transformations of the function
\[f (x) = \frac{ 1 }{ x-6 } + 7\]

Answer 8

how far did you get

Answer 9

i didn't get anywhere. i know this much:
a - stretches the function vertically by |a|
c - stretches the function horizontally by |1/c|
h - moves the graph horizontally
k - moves the graph vertically

but i don't know what numbers are what letters, per say

Answer 10

the basic form is

\[\large f(x) = \frac{a}{c*x - h} + k\]

Answer 11

in this case

a = 1
c = 1
h = 6
k = 7

Answer 12

so a stretches the function by 1, c stretches the function by 1, h moves the graph 6 spaces horizontally and k moves the graph vertically by 7 spaces. correct?

Answer 13

good, so the graph is shifted to the right 6 places and shifted up 7 units

Answer 14

gotcha

Answer 15

@jim_thompson5910 wait a minute, it's -6. so doesn't that make it shift to the left?

Answer 16

no h = +6 not h = -6

Answer 17

notice how it's c*x - h and not c*x + h

Answer 18

so if it was a positive number would it shift to the left?

Answer 19

that -h means your shift will be opposite of what the number is saying

Answer 20

if it was x+6, then yes, it would shift 6 units to the left

Answer 21

because x+6 is the same as x-(-6)

and then you can pick out that h = -6