Question

The graph above is a transformation of the function f(x)=|x|

Write an equation for the function graphed above

Answer 1

@SolomonZelman

Answer 2

@mathstudent55

Answer 3

the function is a translation from the origin. we know because we know what the graph of the absolute value function looks like normally:
http://www.wolframalpha.com/input/?i=%7Cx%7C

Answer 4

also, it is dilated in some way

Answer 5

let's deal with the translation first. the concave point at (-2, -2) has been translated from (0, 0).
how can we do that using f(x) = |x|?

Answer 6

@swagjason1998

Answer 7

I know the function has been shifted to the left by 2 units

Answer 8

It also is either compressed or stretched in some way

Answer 9

@satellite73

Answer 10

it's been shifted left and up by 2 units. to represent this as a function we use:
f(x) = |x+2|+2

now,what about the dilation?

Answer 11

I am not sure what you mean by dilation. Not familiar with that term

Answer 12

@swagjason1998

Answer 13

the function was scaled by some number. we have to find that number. when we do the function will be of the form
f(x) = c|x+2|+2

Answer 14

I see how to find the shift
but how to find the scaling?

Answer 15

in the function |x|, we note that the slope of the positive line is 1
find the slope of the new positive line

Answer 16

where do you see the slope of the positive line?

Answer 17

refer to diagram

Answer 18

the new slope is over 1 and up 1 if I am looking at the diagram

Answer 19

wot

Answer 20

not following you with the slope on a translated function

Answer 21

I know what the abs(x) looks like on a graph

Answer 22

sorry, my intuition for this kinda thing is weird

Answer 23

so, in the function we have to write, what is the slope of the positive line?

Answer 24

and the slope would come before the x

Answer 25

slope of |x| = 1

Answer 26

but we have |x+2| + 2

Answer 27

@swagjason1998

Answer 28

n
slope of positive line in the picture
http://assets.openstudy.com/updates/attachments/537929b2e4b0e54307958a99-jtryon-1400449475969-screenshot20140518at2.25.17pm.png

Answer 29

is that -1?

Answer 30

@mathstudent55 @satellite73 @SolomonZelman

Answer 31

n
look at it & use slope formula

Answer 32

what is n swag?

Answer 33

n = no

Answer 34

that is where I am lost

Answer 35

so pick two points on the line and figure out the slope

Answer 36

slope I got was 1/4

Answer 37

@swagjason1998

Answer 38

yep. scale is 1/4

Answer 39

so now I put that into the translated function

Answer 40

g(x) = 1/4x + 2 + 2

Answer 41

|x+2|/4 + 2

Answer 42

oh I was writing it |1/4x+2|+2