Question

how do you graph this function?please show work! g(x)=5|x-4|+2

Answer 1

There could be a little trick to this but I havent done one like this in a loong time. Start with g(x) = abs(x)

You know what that graph looks like

Then make the transformation to g(x) = abs(x - 4)

and keep going until you got your whole function

Answer 2

That's the best way to do it, imho.

Answer 3

I'm sorry, can you explain it a little more thoroughly Walleye?

Answer 4

Do you know what the graph of\[f(x)=|x|\]looks like?

Answer 5

yes i do

Answer 6

What would happen to that graph if we do this\[f(x)=|x-4|\]

Answer 7

it would move over 4 to the right, right?

Answer 8

Thanks Across, you seem to be very good in math :D

Answer 9

That's correct! Now, what would happen to it if we multiply it by five like this\[f(x)=5|x-4|\]

Answer 10

Aww thank you Walleye :)

Answer 11

I'm not really sure :( sry. i know that the graph is going to move up 2 tho, right?

Answer 12

It is almost the same thing as multiplying\[f(x)=x\]by 5\[f(x)=5x.\]The slope of the line gets "steeper." :)

Answer 13

If i may, think of the function f(x) = x and f(x) = 5x

What happens when you mutiply f(x) = x by 5??

Answer 14

Copycat!

Answer 15

so then it does down 5?

Answer 16

*goes

Answer 17

No, the graph gets "steeper" like this (see attached).

Answer 18

Finally, I'm sure you already knows what will happen to the graph if we add two to it\[f(x)=5|x-4|+2\]

Answer 19

know*

Answer 20

Try graphing all of these functions yourself and you will get a feel for how these transformations affect the function

Answer 21

I got it! Thank you guys so much :) I appreciate it!

Answer 22

No problem!!! Practicing problems like these can be a bore but soon enough you will get good enough to see most any function and know what it looks like right away!!

Answer 23

Lol! it's true, they are a bore :) thanks again!